Extracts from 10 Dots Concerning Providence and Commentary on the Parmentities of Plato by Proclas, translated by Thomas Taylor. This LibriVox recording is in the public domain. Recording by Geoffrey Edwards 1. Another providence extends to all things, to holes and parts, and as far as to the most indivisible natures in the heavens, and in the sublunary regions, in things eternal, and things corruptible. This Proclas affirms and says that every particular, even of the minutest things, depends on the beneficent providence of divinity. For nothing escapes that one, whether you speak of the essence of a thing, or its being known. It is said indeed, and is rightly said, that the whole circle is centrally in the center, since the center is the cause, but the circle the thing caused, and, for the same reason, every number is monadically in unity. But in the one of providence, all things subsist after a more exalted mode, since that is more transcendently one than a center and the monad. 2. How divinity foreknows and provides for things contingent? Proclas answers that divinity, on account of his most perfect nature, knows in their seeds and causes things indefinite, definitely, as he also knows things distant and corporeal, without distance, and incorporeally. 3. Providence is the cause of things definite and indefinite, according to the same and after the same manner. Proclas answers that to provide for is nothing else then to benefit, and that hence everything participates of that one good according to its own measure and order, so that providence retains its unity and liberty, even in things indefinite. In the same chapter also, he proves that divinity provides for things contingent and indefinite, that they may not be, as it were, super-adventitious in the universe, for, says he, if the gods are willing and able to provide definitely for things indefinite, as being the authors of them, they will entirely provide for them, and providing will know the desert of the subjects of their providential energy, and the gods, indeed, with an exempt transcendency extend their providence to all things, but demons dividing their super-essential subsistence receive the guardianship of different herds of animals, distributing the providence of the gods, as Plato says, as far as to the most ultimate division. Hence some of them preside over men, others over lions, or other animals, and others over plants, and, still more partially, some are the inspective guardians of the eye, others of the heart, and others of the liver. All things, however, are full of gods, some of whom exert their providential energies immediately, but others, through demons as media, not that the gods are incapable of being present to all things, but that ultimate are of themselves incapable of participating first natures. For, how the participations of the gods are affected, or how the gods energize providentially on inferior natures? Proclus answers that the participations are according to the aptitude of the participants. We dare leak it. They subsist rationally, in-rational, but intellectually, in-intellectual natures, and imaginably, and sensibly, in those beings that live according to imagination and sense, and they subsist essentially, and through being alone, in those things which are without life. Hence, providence, being established above all beings, according to divine union itself, and energizing according to one energy, adapted to the one, everything which acedes to it participates of it according to its natural adaptation. With respect to the failure of the oracles, he says, that the energy of divinity remaining always the same, places or men become unadapted to its participation. Just as if a certain statue always remaining the same, a mirror should at one time exhibit a folgid image of it, but at another an obscure or debile, or indeed no image of it at all. He adds, if therefore it should be said that oracles sometimes participate of the gods, who are the sources of divination, but at other times fail, becoming inefficacious, and as it were without spirit, for a certain period, the causes of this irregularity must be referred to the vapours that are the instruments of inspiration failing, through an inability of always being the participants of divine influence. For the oracles are true, which give completion to the phenomena, and angels, demons, and heroes are voracious, which the gods and the perpetually existing allotments in the universe illuminate, though certain waters and openings of the earth cannot always participate of them, on account of their unstable nature. Or, if it should be said, that the powers of sacred rites sometimes entering into statues, causing them to be vitalized, and filling them with divine inspiration, fail in certain periods of time, the failure of these also I should think it proper to refer to the recipients, and not to any variation of the energy of the gods that inspire them. For neither do we dare to accuse the sun as the cause of the eclipse of the moon, but the conical shadow of the earth into which the moon falls. 5. Whence and why evil subsists since there is providence? Proclus answers that there are two kinds of evils, one in bodies contrary to nature, the other in souls contrary to reason. The kingdom of providence however says he is molested by neither of them, but to the former of these evils the end is good, and the variety and perfection of the universe. For everything which is preternatural takes place in order that something which is according to nature may be affected, but not vice versa, and with respect to the latter of these evils, between beings more perfect than we are and brutes, it is necessary that souls should intervene as a medium, which are endowed with reason, anger and desire, and rejoice in freedom of will. 6. If providence is, why are good men oppressed with evil, but bad men triumph? Proclus answers that notwithstanding this virtue and the matter of virtue are not wanting to the good, and also that this praise is peculiar to them, that they had rather cultivate naked virtue than vice with all her abundance, that it is not an evil to be deprived of the incentives to evil, that some have even earnestly desired adverse fortune, and that wise men have always borne it with fortitude. Nor is it expedient that wise men should at one and the same time abound with every kind of good, for it is necessary that they should have a certain experience of the evils of the present life, by which the soul, being excited, desires a transition from hence to that place which is beyond the reach of evil. He adds that many, through adversity, have arrived at greater attainments in virtue, and that in short, those things only are evil which we ourselves perpetrate, and not those which we suffer from an external cause. That all bad men are without glory and without honor, though they should be surrounded by thousands of flatterers. To the question which he adjoins to this, why providence distributes equal to unequal things, according to arithmetical, and not according to geometrical equality, as when a whole city perishes, there is a similar destruction of dissimilar men, we dare we get, of the good and the bad, he answers as follows. In the first place, indeed, they do not suffer this similitude of punishment, so far as they are dissimilar, but so far as they are similar, in consequence of voluntarily inhabiting the same city, or entering the same ship, and fighting together, or mutually suffering anything else of the same species. And so, according to the energy of that species, they suffer a certain something which is the same. So far, however, as they are better and worse, they participate differently of the common calamity, since the latter perish, bearing it impatiently, but the former, enduring it mildly. And after a separation from the present life, the place destined to be the habitation of more excellent beings receives the former, but the abode of subordinate beings receives the latter. Proclus afterwards adds that there is a certain order, and a period of common fate, terminating from different principles in the same end, and a concurrence of progressions, where the less principal parts are compelled from necessity to be co-passive, and that we are ignorant of the true equalities of souls. 7. If Providence extends as far as to the lowest beings, whence is the great inequality in the allotments of brutes, their mutual devourations, and the like derived? Proclus answers that if there is anything in them of a self-motive nature, the cause of this must be investigated from a higher source. But if they are only corporeal, it is of no consequence if they suffer the same thing as a shadow, all variously transformed, and are subject to fate. 8. Why punishments do not immediately follow after crimes, but are inflicted at length after the commission of them, and this sometimes is very long after? Proclus answers that the implanted root of wickedness, just as the earth bearing thorns, though the germs are a thousand times cut off, still produces the like, renders the same energies in consequence of continuing inflexible by punishment. Providence, therefore, waits for an appropriate time, not such as maybe pleasing to the vulgar, but such as it knows will contribute to the health of souls, and instructs many by endurance. For together with the gods, says Plato, fortune and time govern all things, whether it be requisite that some good should be imparted, or that there should be a purification from something contrary to good. In the next place, vice is a punishment to itself, and the most grievous injury the soul can sustain. Precipitate anger also is not a good dispensator of punishments. Plato, once being about to chastise a slave, was seen holding his hand in an elevated position for some time, and being asked why he did so, said that he was punishing his own impetuous anger. Architas said to his servants in a field, who had not done what he had ordered them to do, and expected to be punished for their negligence, it is well for you that I am angry, and Theano said to one of her servants, quote, if I were not angry I would chastise you, close quote. Among the Egyptians there was a law that a pregnant woman who was judged worthy of death should not be put to death till she was delivered. What wonder therefore is it that providence should for a time spare those who are deserving of death, but are able to perform not trifling but illustrious actions, till they have accomplished them? If Themistocles had been immediately punished for what he did when he was a young man, who would have delivered Athens from the Persian evils, who also would have explained the Pythian Oracle? If Dionysius had perished in the beginning of his tyranny, who would have freed Sicily, which was thought to be irremediably lost from the Calcedonians? If the punishment of Periander had not been deferred for a long time, who would have freed the pleasant island of Lucadia, who would have liberated an exorium from its adversaries? To which may be added that the time of deferred punishment seems long to our feeble vision, but is nothing to the eye of providence. Just as the place also in which we live and carry about these bodies is perfectly small for the punishment of great offences, but there are many and indescribable places of punishment in the infernal regions and excessive torments for the offenders that are there. On account of the magnitude of the punishment likewise, the whole of it is not inflicted at once. Souls also are naturally adapted to feel remorse, which is the forerunner of their greatest sufferings. For they say that Apollodorus, the tyrant, saw himself in a dream scourged and boiled by certain persons, and his heart exclaiming from the kettle, I am the cause of these thy torments. But Ptolemy, who was surnamed Thunder, thought in a dream that he was called to judgment by Seleucus, and that vultures and wolves sat there as his judges. Such are the preludes to the vicious of impending punishment. 9. How the crimes of other persons, as for instance of parents or potentates, are punished in children and subjects. For that certain persons are sinned to have suffered punishment for the crimes of their ancestors, both revelations and the mysteries manifest, and certain liberating gods are said to purify from them. Proclus answers that a nation or a family or a city must be considered as one body, and that these have kindred powers that preside over them, so that such crimes are not foreign on account of this conjunction and similitude. Why, therefore, should it be any longer paradoxical that souls, when transferred into other bodies, should suffer punishment for the crimes which they have committed in former bodies? 10. Since the providence of divinity knows all things and reduces them to God, how are angels and demons, and, if you are also willing, heroes and souls that govern the world in conjunction with the gods, said to exert a providential energy? Proclus answers that divinity provides for all things universally and totally, but the other powers partially, subordinately, and for certain things only. In order to supply as much as possible the loss of the entire treatise of Proclus on this subject, the following admirable observations on providence are added, translated from his commentary on the permittees of Plato, a work which to the disgrace of Europe is still only extant in manuscript. Quote, The Athenian guest in the Laws clearly evinces that there is a providence where his discourse shows that the gods know and possess a power which governs all things. But permittees, at the very beginning of the discussion concerning providence, evinces the absurdity of doubting divine knowledge and dominion. For, to assert that the conclusion of this doubt is still more dire than the former, Ed est that divinity is not known by us, sufficiently shows that he rejects the arguments which subvert providence. For, it is dire to see that divinity is not known by us who are rational and intellectual natures, and who essentially possess something divine. But it is still more dire to deprive divine natures of knowledge, since the former pertains to those who do not convert themselves to divinity, but the latter to those who impede the all-pervading goodness of the gods, and the former pertains to those who err respecting our essence, but the latter to those who convert themselves erroneously about a divine cause. But the expression, still more dire, denoteran, is not used as signifying a more strenuous doubt, in the same manner as we are accustomed to call those dire, denoi, who vanquish by the power of language. But, as a thing worthy of greater dread and caution to the intelligent, for it divorces the union of things, and dissociates divinity apart from the world. It also defines divine power as not pervading to all things, and circumscribes intellectual knowledge as not all perfect. It likewise subverts all the fabrication of the universe, the order imparted to the world from separate causes, and the goodness which fills all things from one will, in a manner adapted to the nature of unity. Nor less dire than any one of these is the confusion of piety, for what communion is there between gods and men, if the former are deprived of the knowledge of our concerns? All supplications, therefore, of divinity, all sacred institutions, all oaths adducing the gods as a witness, and the untaught conceptions implanted in our souls concerning divinity will perish. What gift also will be left of the gods to men, if they do not previously comprehend in themselves the dessert of the recipients, if they do not possess a knowledge of all that we do, of all we suffer, and of all that we think, though we do not carry it into effect? With great propriety, therefore, are such assertions called dire, for, if it is unholy, to change any legitimately divine institutions, how can such an innovation as this be unattended with dread? But that Plato rejects this hypothesis, which makes divinity to be ignorant of our concerns, is evident from these things, since it is one of his dogmas that divinity knows and produces all things. Since, however, some of those posterior to him have vehemently endeavored to subvert such like assertions, let us speak concerning them as much as may be sufficient for our present purpose. Some of those then posterior to Plato, on seeing the unstable condition of sublunary things, were fearful that they were not under the direction of providence and a divine nature. For such events as are said to take place through fortune, the apparent inequality respecting lives, and the disordered motion of material natures, induced them greatly to suspect that they were not under the government of providence. Besides, the persuasion that divinity is not busily employed in the evolution of all various reasons, and that he does not depart from his own blessedness, induced them to frame an hypothesis so lawless and dire. For they were of opinion that the passion of our soul, and the perturbation which it sustains by descending to the government of bodies, must happen to divinity if he converted himself to the providential inspection of things. Farther still, from considering that different objects of knowledge are known by different gnostic powers, as for instance, sensibles by sense, objects of opinion by opinion, things scientific by science, and intelligibles by intellect, and at the same time neither placing sense nor opinion nor science in divinity, but only an intellect immaterial and pure. Hence they asserted that divinity had no knowledge of any other things than the objects of intellect, and this was the opinion of the more early parapetetics. For, say they, if matter is external to him, it is necessary that he should be pure from apprehensions which are converted to matter. But, being purified from these, it follows that he must have no knowledge of material natures. Hence the patrons of this doctrine deprived him of a knowledge of and providential exertions about sensibles, not through any imbecility of nature, but through a transcendency of gnostic energy, just as those whose eyes are filled with light are said to be incapable of perceiving mundane objects, at the same time that this incapacity is nothing more than transcendency of vision. They likewise add that there are many things which it is beautiful not to know. Thus, to the entheastic, or those who are divinely inspired, it is beautiful to be ignorant of whatever would destroy the deific energy, and to the scientific not to know that which would defile the indubitable perception of science. But others, as the Stoics, ascribe indeed to divinity a knowledge of sensibles, in order that they may not take away his providence, but at the same time convert his apprehension to that which is external, represent him as pervading through the whole of a sensible nature, as passing into contact with the objects of his government, impelling everything, and being locally present with all things. For, say they, he would not otherwise be able to extend a providential energy in a becoming manner, and impart good to everything according to its dessert. Others again affirm that divinity has a knowledge of himself, but that he has no occasion to understand sensibles in order to provide for them. Since, by his very essence, he produced all things and adorns whatever he has produced, without having any knowledge of his productions. They add, that this is by no means wonderful, since nature operates without knowledge, and unattended with fantasy. But, that divinity differs from nature in this, that he has a knowledge of himself, though not of the things which are fabricated by him, and such are the assertions of those who were persuaded that divinity is not separated from mundane natures, and of those who deprived him of the knowledge of inferior concerns, and of a knowledge operating in union with providence. With respect to these philosophers, we say, that they speak truly, and yet not truly, on this subject. For if providence has a subsistence, neither can there be anything disordered, nor can divinity be busily employed, nor can he know sensibles through passive sense. But, these philosophers, in consequence of not knowing the exempt power and uniform knowledge of divinity, appear to deviate from the truth, for thus we interrogate them. Does not everything energize in a becoming manner, when it energizes according to its own power and nature? As, for instance, does not nature, in conformity to the order of its essence, energize physically, intellect intellectually, and so psychically, or according to the nature of so? And, when the same thing is generated by many and different causes, does not each of these produce according to its own power, and not according to the nature of the thing produced? Or, shall we say, that each produces after the same manner, and that, for example, the sun and man generate man, are according to the same mode of operation, and not according to the natural ability of each? We dare leak it, though one partially, imperfectly, end with a busy energy, but the other without anxious attention, by its very essence and totally. But, to assert this would be absurd, for a divine operates in a manner very different from a mortal nature. If, therefore, everything which energizes, energizes according to its own nature and order, some things divinely and supernaturally, others naturally, and others in a different manner, it is evident that every Gnostic being knows according to its own nature, and that it does not follow that because the thing known is one and the same, on this account the natures which know, energize in conformity to the essence of the things known. Thus sense, opinion, and our intellect know that which is white, but not in the same manner, for sense cannot know what the essence is of a thing white, nor can opinion obtain a knowledge of its proper objects in the same manner as intellect, since opinion knows only that a thing is, but intellect knows the cause of its existence. Knowledge, therefore, subsists according to the nature of that which knows, and not according to the nature of that which is known. What wonder is it, then, that divinity should know all things in such a manner as is accommodated to his nature? We dare leak it? Divisible things, divisible things, indivisibly, things multiplied uniformly, things generated according to an eternal intelligence, totally, such things as are partial, and that with the knowledge of this kind he should possess a power productive of all things, or in other words, that by knowing all things with simple and united intellections he should impart to everything, being, and a progression into being. For the auditory sense knows audibles in a manner different from the common sense, and prior to, and different from these, reason knows audibles, together with other particulars, which sense is not able to apprehend, and again of desire which tends to one thing, of anger which aspires after another thing, and of pro-eresis, or deliberate choice, there is one particular life moving the soul towards all these, which are mutually motive of each other. It is through this life that we say, I desire, I am angry, and I deliberately choose this thing or that, for this life verges to all these powers and lives in conjunction with them, as being a power which is impelled to every object of desire. But prior both to reason and this one life is the one of the soul, which often says, I perceive, I reason, I desire, and I deliberate, which follows all these energies and energizes together with them. For we should not be able to know all these, and to apprehend in what they differ from each other, unless we contained a certain indivisible nature, which has a subsistence above the common sense, and which prior to opinion, desire and will, knows all that these know, and desire, according to an indivisible mode of apprehension. If this be the case, it is by no means proper to disbelieve in the indivisible knowledge of divinity, which knows sensibles without possessing sense, and divisible natures, without possessing a divisible energy, and which without being present to things in place knows them prior to all local presence, and imparts to everything that which everything is capable of receiving. The unstable essence, therefore, of apparent natures is not known by him in an unstable, but in a definite manner, nor does he know that which is subject to all various mutations dubiously, but in a manner perpetually the same, for by knowing himself he knows everything of which he is the cause, possessing a knowledge transcendently more accurate than that which is coordinate to the objects of knowledge, since a causal knowledge of everything is superior to every other kind of knowledge. Divinity therefore knows, without busily attending to the objects of his intellect, because he abides in himself, and by alone knowing himself knows all things, nor is he indigent of sense, or opinion, or science, in order to know sensible natures, for it is himself that produces all these, and that in the unfathomable depths of the intellect of himself comprehends and united knowledge of them according to cause, and in one simplicity of perception. Just as if someone, having built a ship, should place in it men of his own formation, and in consequence of possessing a various art, should add a sea to the ship, produce certain winds, and afterwards launch the ship into the new created mean, let us suppose too, that he causes these to have an existence by merely conceiving them to exist, so that by imagining all this to take place, he gives an external subsistence to his inward fantasms. It is evident that in this case he will contain the cause of everything which happens to the ship through the winds on the sea, and that by contemplating his own conceptions, without being indigent of outward conversion, he will at the same time both fabricate and know these external particulars. Thus, and in a far greater degree, that divine intellect, the artificer of the universe, possessing the causes of things, both gives subsistence to, and contemplates whatever the universe contains, without departing from the speculation of himself. But if with respect to intellect, one kind is more partial, and another more total, it is evident that there is not the same intellectual perfection of all things, but that where intelligibles have a total and undistributed subsistence, there the knowledge is more total and indivisible, and where the number of forms proceeds into multitude and extension, there the knowledge is both one and multi-form. Hence, this being admitted, we cannot wonder on hearing the orphic verses in which the theologist says, There, in the sight of Jove, the parent king, the immortal gods, and mortal men, reside, with all that ever was, and shall hereafter be. For the artificer of the universe is full of intelligibles, and possesses the causes of all things separated from each other, so that he generates men, and all other things according to their characteristic peculiarities, and not so far as each is divine, in the same manner as the divinity prior to him. The intelligible father feignies. The admirable dogma in this most beautiful extract quote, that knowledge subsists according to the nature of that which knows, and not according to the nature of that which is known, close quote, was originally derived from Amplicus, as is evident, from the commentary of Amonius on Aristotle's treatise on interpretation. See note to page 162 of my translation of the Organon. Boethius, in the fifth book of his treatise, the Consolatione elegantly illustrates this dogma. The passage I allude to begins with the words, quote, omne enim, quod cognoschitor, non secundum sui wim, sed secundum cognoschentium potius comprehenditor facultatem, close quote. The sources, however, from whence he derived this doctrine appear to have been unknown to all his editors and commentators, for they are not noticed by any of them. End of extracts from ten doubts concerning providence and commentary on the parmenides of Plato. Extracts from the treatise of Proclus on the subsistence of evil. By Thomas Taylor. This LibriVox recording is in the public domain. Recording by Jeffrey Edwards. In this treatise, Proclus inquires first whether there is such a thing as evil. Secondly, if there is, whether it is in intellectual natures. Thirdly, if evil is insensible, whether it subsists according to a principal cause. Fourthly, if it does not subsist according to a principal cause, whether any essence must be assigned to it, or whether it must be admitted to be perfectly unessential and without hypostasis. Fifthly, and if this be the case, how does it subsist another principal existing, and whence does it originate, and how far does it proceed? And farther still, sixthly, how, since providence exists, does evil subsist, and whence is it derived? If the Father of the Universe not only produced the nature of God, but was also willing that there should be nothing evil anywhere, by what contrivance or art does evil subsist, which the Demiurgus did not wish to subsist. For it is not lawful to assert that he was willing some things should subsist, but produced others, since in divine natures, to be willing and to produce are simultaneous and conjoined. Hence, evil is not only a thing contrary to the will of divinity, but is also without hypostasis. Divinity not only not producing yet, for this it is not even lawful to suppose, but not suffering it to subsist. Proclus answers that physical evil, we derrily get, the evil which is corruptive of the essence, power, and energy of a thing, is not evil but good, because it subsists on a count of good, and because generation is from corruption, of which too the world consists, and by which the order of the universe is adorned. There is not, however, such a thing as unmingled evil, and evil itself, or an eternal idea, form and essence of evil. But moral evil is mixed with good, and so far as it is good, it subsists from divinity, but so far as evil, it is derived from another cause which is impotent. For evil is nothing else than a greater or less declination, departure, defect, and privation from the good itself, and which is good alone, in the same manner as darkness from the sun. It is the debility and absence of power in energizing, but is not power, and that which is evil to partial natures is not evil to the universe. 2. Evil is not in the gods, nor in the triple government of the better general, we derrily get. It is neither in angels, for how could we call them messengers, and elucidators of the gods, if evil of any kind was in them who are the images of the divinities, and who dwelling in the vestibules of deity participate of its goodness, nor in demons, nor in heroes. If divinity produced evil, he either produced it contrary to his nature, or everything hence subsisting will be bona form, and the progeny of the goodness that abides in him. But, as it is said, it is not the property of fire to impart cold, nor of good to produce evil from itself. Either therefore it must be said that evil is not, if it is necessary to its existence, that it should be produced by divinity, or that it is, and does not originate from deity. Against those who assert that evil is primarily in demons, he observes as follows. There are certain persons who attribute passions to demons, and say that some of their passions are according to nature, as when they tragically speak of their deaths, and different generations, but that others are from choice only, as when they denominate certain demons base and evil, who they also say defile souls, lead them to matter, and draw them down from their journey to the heavens to the subterranean region. It is necessary, however, to ask these persons whether are the demons which you say are evil, such to themselves, or in their own nature, or not to themselves, but to others. For if they are evil to themselves, one of two things must follow, either that they must remain in evil forever, or that they must be susceptible of transmutation. And if indeed they are always evil, how can that which subsists from the gods be perpetually evil? For it is better not to be at all than to be always evil. But if they are transmuted, they are not essentially evil, but are evil from habitude, in which there is the better and the worse, and another species of life. Demons, however, are always in the ratio of demons, and each of them is always in its own order. But if they are indeed good to themselves, but evil to others, whom they lead into a worse condition, it is just as if someone should call teachers depraved, and certain pedagogues, who ranking as the chastisers of offenses, do not suffer the offenders to pursue a better order in a fluctuating manner, instead of an order which is adapted to them. Or as if someone should denominate those officers evil, who, standing before things of a sacred nature in temples, keep the impure from entering into the sanctuary, because they prohibit them from the participation of the interior rites.  If, therefore, of the demons that are in the world, some lead souls upward, but others keep such in their own manners, as are not yet able to ascend, we cannot justly call either of them evil, neither those that separate from, nor those that detain souls in a corporeal life. For, it is necessary, that there should also be those demons who coerce the soul that is defiled with vice, and is unworthy of a progression into the heavens, in the place which surrounds the earth. Neither, therefore, in these, does reason appear to discover evil, for whatever they do, they perform according to their own nature, and always after the same manner, but this is not evil. 3. Evil in souls is a debility of not always and uniformly adhering to better natures and to God. Hence arises their descent to things subordinate, their oblivion, their malefic inclination to things conversant with body, and their discord with reason. 4. According to some, matter is that which is primarily evil and evil itself, and the debility of souls arises from their laps into matter. This, Proclus denies, and says that both body and matter originate from deity, and that both are the progeny of divinity. He adds that matter is the first indefinite, and that essential infinity, in the same manner as a mixed body, depends on one cause, divinity, that souls sinned before they were thrust into matter, that there are not two principles, matter and deity, and that matter is neither good nor evil, but a thing necessary and distant in the last degree from the good itself. 4. Of good there is one eternal, definite, universal and producing cause, we dare liket God, but of evils the causes are manifold and infinite, some to souls and others to bodies. They are also fluctuating, indefinite, inordinate, and particular, surrounding the nature of souls and bodies from necessity, and arising from impotency, incommensuration void of design, unadaptation, debility, and the victory of subordinate nature. Good has an hypostasis, but evil a pair hypostasis, or a deviation from hypostasis. Good is form, but evil is without form and is, as it were, privation. 5. Evil possesses its power of acting, and its capability from a contrary good, which becomes debile and inefficacious on account of the mixture of evil, and evil is allotted its efficacy and energy on account of the presence of good, for both are in one. Thus, in bodies, that which is preternatural debilitates that which is according to nature, the energy of nature being in this case dormant, and order in which good consists being dissolved. Thus also in souls, evil, when it vanquishes good, uses its power, we dare liket the power of reason to its own purposes, and makes it subservient to desire. Each of these also imparts something according to its own nature, we dare liket the one power, but the other, debility, because of itself evil is neither adapted to act nor to possess power, for all power is good, and all energy is an extension of power. And this, Plato knowing, says, that injustice itself is of itself debile and inactive, but through the presence of justice possesses its power, and is led forth into energy, not abiding in its own nature. Nor does evil alone consist in a privation of life, because being which subsists prior to life gives also to evil a participation of life. All life, however, is of itself power, but evil subsisting in a foreign power is contrary to good, employing its own power for the purpose of opposing good, and the more power indeed is inherent in it, the greater are the energies and works of evil, and the less it possesses of power, the less are its energies and works. In bodies too, as soon as the powers of nature cease, the preternatural energy which is in them ceases also, and hence all order is entirely dissolved, that which is preternatural being more abundant. When the soul therefore receives an increase from that which is contrary to good, according to its base and formless nature, but is diminished according to virtue and energy, then it becomes at the same time debile and inefficacious, for the augmentation is not then from power, that the transition might be to something greater, but it arises from the presence of the contrary to power, just as if frigidity should use the power of heat to the accomplishment of its own work, vanquishing and subjecting its power. The soul therefore being deficient through the absence of good, and possessing more of privation in proportion as it has more of deficiency, becoming also more debile in its energies through a diminution of virtue, is indeed more evil, but performs less. And how indeed could the increase since it is evil be from power, if the work of all power is to preserve that in which it is, but evil dissipates everything of which it is the evil, hence evil is of itself inefficacious and impotent. If also as Plato says it is involuntary, it will not be the object of the will, and thus it will be a privation of the first triad of the good, we'd add a liquet of will, power and energy. For good indeed is the object of the will, and is in its own nature powerful and efficacious, but evil is unwished for, is debile and inefficacious. For that is not the object of the will to anything which is corruptive of it, nor does power wish for that which may corrupt it, nor does energy wish not to have its hypostasis according to power, but evil is desired in consequence of appearing to be good, and we say that evil seems to be an object of the will on account of the mixture of good with it. Power, therefore, and energy are apparently in evil, but are not so in reality, because they are not essentially inherent in it, nor so far as it is evil, but they extrinsically accede to it, as that to which a pair of hypostasis belongs. Hence, as it appears to me, this is what Socrates shows in the Theotitas to those who are able to understand his meaning. We'd add a liquet that evil is neither privation, nor the contrary to good. For privation is not able to affect anything, nor does it in short possess any power, nor does that which is contrary to good of itself possess either power or energy. But he denominates evil in a certain respect sub-contrary to good, because of itself indeed, or essentially it is privation, yet because it is not altogether perfect privation, but in a similar manner with habit changes from capacity, it is from sense constituted in energizing in the part of contrariety, and is neither perfect privation, nor contrary, but sub-contrary to good. 7. There are these three things which may debilitate, and in which there is evil. We'd add a liquet, a partial soul, the image of soul in animals, and body. The evil to body is to have a preternatural subsistence. The evil to the image of soul is to be in a state of deviation from reason. And the evil to soul, id est to the rational soul, is to deviate from intellect. The defect of life according to reason is the malady of this life, but ignorance and a privation of intellect are baseness. Whether this takes place about the dynoetic or the doxastic power, and if about the former, it is a want of science, but if about the latter of art. Baseness, however, and malady subsist in one way in cognitions, and in another in impulses. For the irrational appetites are hostile to the life which consists in action, and the many senses, and precipitate imaginations, intervening in the contemplative energy, destroy its purity and immateriality. Hence, unbecoming imaginations, or evil consent, and base choice arise, either from an external source, and in various actions, or internally according to anger and desire. That also which is preternatural is to fold. For in the body it is either deformity, as in monsters, or malady, in consequence of the order and commensuration of the body being dissolved, as in corruption, disease, and pain. In many persons, mediated evil, and which abides culturally within the soul, is benefited as being base and unbecoming. But when it subsists in energy, the quality of it becomes apparent. It is manifested, however, by penitence, and the consciousness of the soul. For the medical art also, in the opening of ulcers, and leading forth externally, the inwardly concealed cause, which produced the malady, exhibits an image of the operations of providence, which permits base needs and passions, in order that the perpetrators of them being changed from the habit which they have acquired, and which is inflated with evils, may assume the principle of a better period and life. But whatever passions are within the soul are attended with this good. That they always lead the soul to a proper condition, her improper choice being accompanied with punishment. Thus also the law which is in souls leads each to its appropriate state, and to that dessert which is derived from providence. 9. Evil cannot exist if it is admitted that it is not contrary to good, because all things, and even evil itself, are for the sake of good. Divinity, therefore, is not the cause of evil. For evil, so far as evil never originates from sense, but from other causes, which as we have said generate not according to power, but on account of debility. Hence it appears to me that Plato, when he places all things about the king of all, and says that all things are for his sake, even things which are not good appearing to be good, and in a similar manner belonging to beings, calls him the cause of everything good, and not at once the cause of all things, for he is not the cause of evil, but is the cause of every being, and of everything so far as it is good. If, therefore, we assert these things rightly, all things will be from providence, and evil will have a place among beings. Hence also the gods produce evil, but they produce it as good, and they know, as possessing a unical knowledge of all things, partables impartably, evils according to the form of good, and multitude according to the form of the one. For there is one knowledge of soul, another of an intellectual nature, and another of the gods themselves. For the first of these indeed is a self-motive, the second an eternal, and the third an indivisible and unical knowledge, knowing and producing all things by the one, and of extracts from the Tweetus of Proclus on the subsistence of evil. Extract from commentaries of Proclus on the Tymias by Proclus, translated by Thomas Taylor. This Liebervox recording is in the public domain, recording by Jeffrey Edwards. For the further information of the reader on this most important subject, the subsistence of evil, the following admirable extract is added from the commentaries of Proclus on the Tymias, page 112. The comment is on these words, quote, divinity, being willing that all things should be good, and that as much as possible, nothing should be evil, close quote, and is as follows, quote. The divine fabrication and intellectual production proceeds from things impartable to such as are partable, from the united to the multiplied, and from things without interval to corporeal masses that are every way distended with interval. This also, the discourse about it, atom-braiding, in the first place, enunciatively celebrates the final cause, afterwards, discursively, and in the third place, delivers in an evolved manner the whole orderly distribution and progression from it. For the words, quote, he was good, close quote, uniformly indeed comprehend everything final, and the most divine of causes, but the words, quote, in that which is good, envy is never inherent about anything, and being without this he was willing that all things should be generated as much as possible, similar to himself, close quote, effect this discursively. For, after the one will of intellect, he introduces the divided contemplation of it, and in the present words, he delivers to us the intelligence of divinity, now proceeding into all multitude and interval, evolving every demuregic providence and all the parts of fabrication. Moreover, the third of these is in continuity with the second, and the second with the first, for since the first particle was, quote, he was good, close quote, On this account the second begins from the good, but proceeds as far as to the will of the father, but the third, beginning from will, delivers the whole of his providential energy. For, if he was good, he was willing to make all things good, but if he was willing, he made them to be so, and led the universe into order, for providence indeed is suspended from will, but will from goodness, and thus much concerning the order and connection of the words. Let us, however, consider what this will is, in order that we may understand how it is conjoined with goodness. Superessential union itself, therefore, and which is of itself exempt from beings, is indeed one, ineffable, and indefinite, having the uncircumstribed and the incomprehensible in the one itself. If, therefore, it be requisite to survey in this the above mentioned uniform triad, goodness indeed has the precedency, but will is the second, and providence is the third, goodness indeed producing the perfect, the sufficient, and the desirable, but will exhibiting exuberant plenitude, the extended, and the generative, and providence imparting the efficacious, the perfective, and the undefiled. According to this ineffable and united parxies of the triad, the intelligible also is triply divided into essence, power, and energy, essence indeed being firmly established in it, and being self-perfect, but power having a never-failing and infinite progression, and energy being allotted perfection and essential production, and again, intellect after the same manner is triply divided into being, life, and the intellectual. For the first of these indeed is the supplier of its existence, the second of its life, and the third of its gnostic power. After these also, soul is divided into that which is the object of science, into science, and into that which is scientific. For the first of these is that which is known, the second is knowledge, and the third is that which derives its completion from both these, these triads therefore being for, as goodness is to will, so is essence to power, being to life, and the object of science to science, and as will is to providence, so is power to energy, life to intellect, and science to that which is scientific. For essence, being, and the object of science have an order analogous to goodness. For the connective, the stable, the uniform, and the perfective pertain to goodness, but power, life, and science are analogous to will. For the self-begotten, and that which comprehends and measures all things, belong to will, and energy, intellect, and that which is scientific pertain to providence. For the efficacious, and that which proceeds through, and antecedently comprehends all things, are the resemblances of divine providence. Since therefore the Demiurgus also is a god, and an impertisable intellect, so far as he is a god indeed, he possesses goodness, will, and providence, but as intelligible he has essence, power, and energy, and as intellect he is, and has life, and a knowledge of holes. The monad also, which he possesses, is suspended from unity, and thus much concerning will. Consequent to this it remains to inquire how the Demiurgus wished all things to be good, and if this is possible, and in what manner. For it may be said, if he was willing, that this should be the case, it would be requisite, that the progression of things should stop at the gods, and undefiled essences. If, however, he not only fabricated these, but also brutes, and reptiles, and men, and everything material, he was not willing that all things should be good. For he was not willing that better natures should exist, but also fabricated such as are worse. If he had been willing therefore that all things should be good, he would have stopped his fabrication at the gods. We reply, however, that if the progression of things was only as far as to the gods, all things would not be good. For, first natures, being allotted the last order, the good would be destroyed, since being able and willing to generate, through their goodness, yet in consequence of an arrangement as the last of things, they would become unprolific and not good. Our opponents therefore say, if all things are good, the progression is as far as to the gods. But we say, if the progression of things extends only as far as to the gods, all things are not good. For if a divine nature is unprolific, how is it good? But it will be unprolific, if it is the last of things. For everything which generates is better than that which is generated, but the less excellent nature not existing, that which is more excellent will have no subsistence. Let there be the gods therefore, and let them have the first order. But after the gods, let there be a progression as far as to matter itself, and let us give a transition to all beings, from the first to the last of things. And neither let there be anything wanting, even of the last of beings, nor any vacuum. For what vacuum can there be, when things characterized by itself have the first subsistence? Those that rank as the second proceed from these. Those of the third order proceed from these and others. Those in the fourth rank are generated from things characterized by the term another, and those in the fifth rank being others only. And on each side of these, those natures subsisting, which are dissimilarly similar. Such therefore, being the continuity in things, what can be deficient? Immovable natures being first established, self-motive natures having the second, and alternative natures the third rank, all of which are the last of things. For all beings derive their completion from the above-mentioned orders. In short, the production of things may be shown to be continued in many ways, and if you are willing, so to speak, analogy subsisting from on high, as far as to the last of things, according to the well-ordered progression of all beings from the one. Let, therefore, all these things be acknowledged, and let the generation of beings be extended as far as to nothing. But whether is there nothing evil in these, or shall we admit that there is in a certain respect, and that there is what is called depravity in bodies and in souls. For some have been led by this doubt to take away evil entirely, but others have been induced to deny a providence in consequence of believing that if providence has a subsistence, all things are good. For if indeed divinity was willing there should be evil, how can he be good? For it is the province of that which is essentially good to benefit everything, just as it is of that which is essentially hot to give heat. But it is not lawful for the good to affect anything else than what is good. And if divinity was not willing there should be evil, how can it have a subsistence? For something will exist contrary to the will of the Father of all things. Such, therefore, is the doubt. We must see, however, conformably to the doctrine of Plato, according to our preceptor, that the habit of divinity with respect to things subsists in a different manner from that of ours. And again, that the habit of things with reference to divinity is different from their habitude with reference to us. For holes have a relation to parts different from that of parts to each other. To divinity, therefore, nothing is evil, not even of the things which are called evil. For he uses these also to a good purpose. But again, to partial natures, there is a certain evil, these being naturally adapted to suffer by it. And the same thing is to a part indeed evil, but to the universe and to holes is not evil but good. For so far as it is a being, and so far as it participates of a certain order, it is good. For this thing which is said to be evil, if you apprehend it to be destitute of all good, you will make it to be beyond even that which in no respect whatever is. For as the good itself is prior to being, so evil itself is posterior to the nothingness of non-entity. For that which is most distant from the good is evil, and not that which has no kind of subsistence. If therefore that which in no respect whatever is has more of subsistence than evil itself, but this is impossible, it is much more impossible that there should be such a thing as evil itself. If however that which is entirely evil has no subsistence, but evil is complicated with good, you give it a place among beings, and you make it good to other things. And indeed, how is it possible it should not, if it ranks among beings? For that which participates of being participates also of unity, and that which participates of unity participates likewise of good. Hence evil, if it is, participates of good, because evil has not an unmingled subsistence, and is not entirely deprived of order and indefinite. Who therefore made it to be such? Who imparted to it measure and order and bound? It is evident that it is the Demiurgus who rendered all things similar to himself, for he filled both holes and parts with good. But if he benefits all things, and colors evil itself with good, there is nothing evil according to the power of divinity and of recipients, for power is to fold, one being that of divinity which benefits the depravity that is so abundantly seen, but the other being that of recipients which participate of the goodness of the Demiurgus according to the measure of their order in the scale of beings, in consequence therefore of the Demiurgus being willing that there should be nothing evil, nothing gives evil. But if certain persons accuse him as the cause of evil because he gave subsistence to partial natures, they take away the fabrication of the world, subvert the prolific power of holes, and confound the nature of things first and last. That we assert these things however conformably to the opinion of Plato may be easily seen from his writings, for in the Politicus he clearly says, quote, that the world obtained from its maker all beautiful things, but from its former habit all such injustice and evil as are produced within the heavens, close quote. For because there is generation and also corruption, that which is preternatural has a subsistence, and because the deformity of matter fills partial souls with inelegance through an association with it, on this account that which is not conformable to reason is allotted a certain resemblance of subsistence. At the same time however, all these particulars become beautiful through the goodness of the maker of the universe. But in the Republic Plato assigns no other cause of good than God, and says that certain other causes of evils are to be investigated, through which he manifests that evils do not derive their subsistence from divinity, for it is not, says he, the province of fire, to refrigerate, nor of snow to heat, nor of that which is all good to produce evil, and he asserts that certain partial causes of these are to be admitted, and such as are indefinite, for it is not in evils as in things that are good, we dare leak it, that the one, and what is primarily good, precede multitude, and this on account of the indefinite diffusion of evil. The words others therefore, and certain, evince that the causes of evil are partial and indefinite. But in the Theotitas he says, quote, that it is neither possible for evils to be abolished, nor for them to be in the gods, but that they revolve from necessity about the mortal nature, and this place of our abode. If, therefore, evil revolves necessarily in the mortal place, it will not be according to Plato, that which in no respect whatever has a subsistence, and which is exempt from all beings, so that according to him evil exists, is from partial causes and is benefited through the bona form providence of the Demiurgos, because there is nothing which is entirely evil, but everything is in a certain respect accomplished conformably to justice and divinity. For we may make the following division of all that the world contains, some things are holes, but others parts, and of parts some eternally preserve their own good, such as a partial intellect and partial demons, but others are not always able to preserve their proper good, and of these some are alter motive, but others self-motive, and of self-motive natures, some have evil established in their choice, but in others it terminates in actions. With respect to holes, therefore, they are perfectly good, supplying not only themselves, but also parts with good. Such things, however, as are parts, and yet preserve their own good, possess good secondarily and partially. But such, as are parts and alter motive, deriving their subsistence from other things, are suspended from the providence of them, and are transmuted in a becoming manner, as is the case with such bodies as are generated and corrupted. For, if it is necessary that there should be generation, it is also necessary that there should be corruption, for generation subsists according to mutation, and is a certain mutation, but if there is corruption it is necessary that the preternatural should be secretly introduced. As, therefore, that which is corrupted is indeed corrupted with reference to itself, but is not destroyed with reference to the universe, for it is either air or water or something else into which it is changed. Thus also, that which is preternatural is indeed with respect to itself disordered, but with respect to the universe has an orderly arrangement. For, if, though it should be destroyed and entirely deprived of order, it would not dissolve the order of the universe, how is it possible that when having a preternatural subsistence, which is of itself nothing when deprived of all order, it can destroy the whole arrangement of things. But again, partial natures, which are self-motive indeed, and whose energy is directed to externals, cause that which is affected by their energy to be evil to themselves. Yet in a certain respect, this also is good and conformable to divinity. For, since impulses and actions are from choice, actions follow elections according to justice, when he who chooses not only deserves the retribution consequent to his choice, but that also which follows from his conduct. And, simply indeed, the action is not good.  For of gods, some are good to all things, others to such as differ according to species, and others to individuals so far as they are individuals.  Whether, therefore, the action is intemperate or unjust, to those who perform it indeed it is good, so far as it is conformable to justice, but simply it is not good, nor to those by whom it is done, but is to them the greatest evil. And so far as it proceeds from them and is directed to them it is evil, but so far as it proceeds from the universe to them it is not evil.  Let us, however, direct our attention to what remains. We dare leak it to such partial natures as energize self-motively, and who stop their depravity as far as to their choice, for they suffer the punishment of their cogitation alone. For, as it is said, there is a certain punishment of mere imagination, impulse, and will, since the gods govern us inwardly, and as they reward beneficent choice, so likewise they punish the contrary. But, it may be said, how can choice itself have that which is conformable to justice and divinity? May we not reply, because it is necessary there should be an essence of this kind, and a power of an ambiguous nature, and which verges to different lives. If, therefore, that which has dominion over choice is from divinity, choice also is from divinity, and if this be the case, it is good. For the electing soul alone is transferred to another and another order. For all choice either elevates the soul, or draws it downward to an inferior condition of being, and if indeed the choice is from a depraved soul, it is evil. But if it transfers that which chooses to its proper order, it is according to justice and good. For the choice itself introduces punishment to the electing soul, or rather, the choice becomes punishment in him who chooses, causing the soul to apostatize from good. For, as a beneficent choice becomes truly the reward of itself, so a depraved choice becomes its own punishment. For this is the peculiarity of self-motive powers. Hence there is no evil which is not also in a certain respect good, but all things participate of providence. If, however, certain persons should ask on what account an evil-producing cause had at first a subsistence, though it should not rank among holes, but is of a partial nature, to thee it must be said that the progression of beings is continued, and that no vacuum is left among them. Whether, therefore, is it necessary that there should not be every self-motive life, but we shall thus take away many natures that are divine, or shall we say it is necessary there should be holes that are self-motive, but there is no necessity there should be self-motive parts? But how is it possible they should be holes if deprived of their proper parts? And how will the continuity of beings be preserved, if holes and self-motive natures have a prior existence, and also partial and alter-motive natures? But we entirely destroy the intermediate natures, we dare liquant, such as our self-motive indeed, but at the same time partial, and which through the partial form become connected with habit-tuned, but through the self-motive power are at a certain time liberated from habit-tuned. It is necessary, therefore, that there should be this life also, which is a medium in beings, and the bond of things which have, as it were, an arrangement, contrary to each other. Evil, however, is not on this account natural to the soul, since she is essentially the mistress of her choice. For the animated body has an essential tendency to disease, for it is essentially corruptible, and yet disease is not according to nature. Hence disease is indeed evil to the partial nature which is allotted to connect this particular body, but is good to the wholeness of bodies. For it is necessary that what is generated from other things should be changed into another thing. As, therefore, to the nature which is in us, it is good for the nutriment to be changed, in order to the preservation of the animal. Thus also, to every nature, it is good for a part to be corrupted in order that the holes may be preserved, which are always prior to parts. For if parts were generated from holes, and the things generated should remain, all things would be rapidly consumed in consequence of holes becoming partial natures. For a continued ablation taking place from things of a finite nature, the hole must necessarily fail. But holes, not existing, either generation will be stopped, or mutation to partial natures will be derived from other things. Hence that which is evil to a partial nature is good to the whole life of the world. Farther still, therefore, resuming the inquiry after another manner from the beginning. If we are asked whether divinity was willing there should be evil, or was not willing, we reply that he was both, for he was willing indeed, considered as imparting being to all things. For everything in the universe which has any kind of being proceeds from the Demiurgic Cause. But he was not willing, considered as producing all things good. For he concealed evil in the use of good. And if you are willing to argue physically, evil is produced essentially indeed from a partial soul. But accidentally from divinity, so far as it is evil, if it is admitted that divinity gave subsistence to the soul. Evil also, so far as it is essentially good, originates from a divine cause, but accidentally from the soul. For so far as it subsists according to justice, it possesses good. Again, Plato in the Laws defines what punishment is. We dede liquet that it appears to consume him who suffers it, and resembles the opening of ulcers. And he, who is incapable of being healed without a certain action, is incited to the performance of it, in order that the soul, being liberated from her parturiancy, and stupid astonishment about that which is base and repenting of her own evils, may begin to be purified. For base and unjust actions, when they are the objects of hope, are lovely to those that vehemently admire them. But when accomplished, feel those that perform them with repentance. And when indeed they are the subjects of mediation, they cause the soul to be latently diseased. But when they have proceeded into energy, they demonstrate their own imbecility, but liberate the soul from the most disgraceful parturition. And some indeed exhibit this punishment according to the whole of their life, but others according to partial energies. For he who does anything irrational does it from choice, is impelled to that which is the object of his choice, and leads into energy that which pre-existed in his imagination. In short, evil is neither in intellectual natures, for the whole intellectual genus is free from all evil, nor in whole souls or whole bodies, for all holes are exempt from evil as being perpetual and always subsisting according to nature. It remains therefore that it must be in partial souls or in partial bodies, but neither is it in the essences of these, for all their essences are derived from divinity, nor in their powers, for these subsists according to nature. Hence it remains that it must be in their energies. But, with respect to souls, it is neither in such as are rational, for all these aspire after good, nor in such as are irrational, for these energize according to nature. But it subsists in the privation of symmetry of these, with reference to each other. And, in bodies, it is neither in form, for it wishes to rule over matter, nor in matter, for it aspires after the supervening ornaments of form. But it consists in the privation of symmetry between form and matter, from which also it is evident that everything evil exists according to a peripostasis, or resemblance of subsistence, and that at the same time it is colored by good, so that all things are good through the will of divinity. And, as much as possible, nothing is destitute of good. For, it was not possible that generation existing, evil also should not have a shadowy subsistence, since it is necessary to the perfection of the whole of things. And, from what has been said, it is evident that the will of divinity is not vain. For all things are good with reference to him, and there is not any being which is not vanquished by a portion of good. Nor are the words, quote, as much as possible, close quote, written superfluously, for they do not signify an imperfect power, but that power which rules over all things and benefits all things through an abundance of good. Close quote, the end, end of extract from commentaries of Proclus on the timeus, and end of the elements of theology by Proclus, translated by


this question. Let's not talk about the next question here. Okay, a typical question. Find the equation of a plane passing through A, B and C. Also find a unit vector perpendicular to this plane. A very stereotypical question. Okay, you must know how to solve these because much more difficult questions will be framed using these simpler concepts. You can again type the answer privately to me or send me a WhatsApp. Sir, I sent it to you. Yeah, yeah. Can you send me something like an equation? It doesn't look like an equation. Yes, Ardhara is absolutely correct. Aditya, do send me a Cartesian equation. Sir, is it 1 by root of 38 of 5i cap plus 2j plus 3k. Equal to something, right? Or plus something equal to 0. Equation means something has to be equal to, right? Sir, that is n vector like that. You have mentioned the equation of the unit vector, right? Yes, sir. The unit vector is correct. I want the equation first. And that too also there is a small mistake. Aditya, in the sign of k that you have written. Okay. Just check. Yes, sir. So there are two parts to the question. One is the equation of the plane and other is the unit vector perpendicular to this. So if you get one, I think the second one will be easier to find out. Yes, I'll send the equation. Sir, I had sent it to you. Yes, yes. That's correct. Yeah, absolutely correct. Aditya, also correct. Just write 5x and 2y. Okay, now let's discuss this very simple question. Let's do this in Cartesian form. Now remember when you have been given three points on the plane, let's say three non-colonial points first of all, because when you have a collinear point, they can be infinitely many planes passing through it. But when you have three non-colonial points, you can only have a unique plane passing through it. So let's say x1 has coordinate, a has coordinate x1, y1, z1, b has coordinates x2, y2, z2 and c has coordinates x3, y3, z3. I had already discussed with you that we use the concept of coplanarity, correct? Coplanarity whenever the word comes, scalar triple product must appear in our mind. And when you talk about scalar triple product, we talk about coplanarity of three vectors. So I'll take another point, let's say r, x, y, z, okay? And I claim to say that this vector, this vector, and this vector. So basically I'm saying ar vector, ac vector, ab vector, they are coplanar, correct? That means the i, j, k components of these vectors written in determinant form should be zero. So what is the i, j, k component of ar vector? x minus x1, y minus y1, z minus z1. What is the x, y, z component of ac vector? x3 minus x1. Again, you can write ab first, but it doesn't really matter. You can write in any one of the rows, any one of them because ultimately you're equating it to zero. So let me write ab first just to maintain an order of one, two, three. So y2 minus y1, z2 minus z1, zx3 minus x1, y3 minus y1, and z3 minus z1. Now let me tell you it doesn't really matter which three vectors you are taking and writing their stp as zero.  But r must be there, else your equation will not be there. So take any three vectors formed by these four non-colonial points, in fact four coplanar points to be more precise. So when you use this in our given problem, so let's take our x1, y1, z1 to be our point c because it looks simpler of all. x minus 7, y minus 0, z minus 6. And take the difference of any two points you want, doesn't really matter. So let's say I take the difference of ab, so I get a 1, I get a 2, I get a 3, then I take the difference of bc, let's say.  Equated to zero. Just drop the factor of 4 throughout just to save our time. So I'll make it as 1 minus 1 and 1. 1 minus 1 and 1. And let me expand it, so it's x minus 7 times 2 plus 3 which is 5, minus y times 1 minus 3 which is minus 2, and z minus 6 times minus 3 equal to 0. So if you expand it, you get 5x plus 2y minus 3z and constants will be minus 35, minus 35 plus 18 which is minus 17 equal to 0, that becomes the answer of the question. If you want to write it in the vector form, you can write it as r dot 5i plus 2j minus 3k is equal to 17 or minus 17 equal to 0. So this is the vector form. Now they're asking a unit vector along the normal, just take this vector and divide by the magnitude of this vector which is under root 25 plus 4 plus 9, that's 5i plus 2j minus 3k over root 38. Make sense? Okay. Now a very interesting thing that we can also discuss when we are talking about equation of a plane passing through three points. So let's say I have these three points a, b and c. These are my three non-colonial points. Now when I say these three points form a plane, that means they are coplanar, correct? So can I say any, let's say I take any generic point r, can I say r minus a vector is coplanar to is coplanar to, is coplanar to, let's say b minus a and c minus a vector, correct? Now you could have written that also in another form without stp, that is you could have written r minus a vector as x times b minus a plus y times c minus a. Now remember our first discussion on coplanarity of points was based on expressing a vector, let's say a, b, c, r, 3 vectors which are coplanar, then one can be expressed as a scalar combination or the linear combination of the other two. So this vector is coplanar to this and this. So it could be expressed as a linear combination of other two. So x and y here are some scalar quantities. Do you remember this? All of you remember this? Yes or no? Yes. Yeah, so there's another way that you can actually represent the equation of a plane which is having a point a, b, c on it is a plus xb minus a plus yc minus a, okay?  Is that fine? Correct? Now you could also choose to do away with one of the constants. You can choose your one of the constants as a 1 and make this as a plus some lambda b plus some mu c. Are you getting it? Okay. So this is another form of the equation of a plane but this is very less used. I mean you will not see this in at least your NCRT books, okay? In some international books, yes, they talk about it but you will not find them in your NCRT book. Are you getting my point? So you could also write down the equation of a plane passing through three points in this form. This is called by the way a parametric form because lambda and mu are parameters over here because as lambda and mu change, then only you get different, different points on the plane. Are you getting it? So if I give you an equation which is in this form, will you be able to write a Cartesian form for it? Let's take a question on this. So there is an equation of a plane given like this. Following plane it should be not planes in Cartesian form. So basically they have given you an equation in this form. r is equal to a plus lambda b plus mu c.  So these are coplanar points. It's just another way of saying it. That means they all lie on a plane. Please reply privately to me once you're done. No Shreya. Oh, you may be correct also. By the way, let me write it like this. r minus this. Send it to you sir. Send it to me? Yes sir. Yes. So r minus a vector is coplanar to b and c. That's what I'm trying to say.  Just so you open the bracket, it'll become plus j. So it becomes x minus 1i, y minus 1j and zk. So this will come in your first row. So x minus 1, y minus 1, z will come in the first row. The other two vectors, b and c vectors will come in the second row. 1, 1, 1, 1 minus 2, 3. Okay. Getting the point. So when you expand this, it becomes x minus 1, 3 plus 2, which is 5, minus y minus 1, which is 3 minus 1, which is 2, and z times minus 3 equal to 0. When you expand it, you get 5x minus 2y minus 3z.  Is that fine? Everything is okay so far. Sorry, there is no. So wanted to y plus 1. Y plus 1. Y plus 1. Ah, yes, yes, yes, yes. This is y plus 1. I'm so sorry. Yeah, y plus 1, plus 1. So it will become a minus 2 here. This will not be there. This is minus 2. So if you expand it, it becomes this. Okay. Now, whenever you are in confusion, there's another way to deal with it. You can just write it as xi plus yj plus zk and compare both the sides. See, another way of doing it, but probably a slightly lengthier way to do it.  Okay. So what I'll do is first I'll write my r as xi plus yj plus zk. Okay. And I'll compare and I'll compare my i coefficients, j coefficients and k coefficients on both the sides. So x is equal to 1 plus lambda plus mu. Y is equal to minus 1 plus lambda minus 2 mu and z is equal to lambda plus 3 mu. Now, from here, I have to eliminate my lambda and mu. So what I'll do is I'll take any two of the equations. Let me take the first two, not first two, first and the last. Okay. So let me subtract it first. So when I subtract x minus z is equal to 1 minus 2 lambda, sorry, 2 mu. Correct.  Okay. Put it in the last one. So lambda is going to be z minus 3 mu. Mu is 1 minus x minus z by 2. Okay. So once you know these two values, put it in the second equation. So y is equal to minus 1 plus lambda. Lambda is going to be z minus 3 by 2 1 minus x minus z minus 2 mu. So minus 2 mu will be just minus 1 minus x minus z. Okay. And just simplify this further.  So minus 1 minus 1 will become so y is equal to minus 2 minus 2. Just correct me if I missed out on anything. This will become z will become 5 z by 2 plus z. Sir minus 3 by 2 and it's 3 by 2 x. So they won't cancel. Oh, my mistake. My mistake. So I'm sorry. I didn't see that x. I'm sorry. Yeah. So minus 2 and minus minus 2 and plus 3 by 2 I have right now minus minus everywhere. So it's minus 7 by 2. So this is going to be minus 7 by 2. So let me just remove the constants from everywhere and z term would be 5 z by 2 plus plus 2. So 7 z by 2 7 z by 2. So Z Z gone. And one more that is there. Okay. And you have 3 by 2 x and y is on the other side. So multiply with the 2 and bring the y on the other side so it becomes 3 x minus 2 y plus 3 z. Why am I getting 7 z 2 z 5 z just check if the values are correct x plus lambda plus mu. That's correct. So why is equal to minus 1 plus lambda minus 2 mu. That's also correct. And z is k lambda plus 3 mu. That's also correct. And if you subtract it becomes 1 minus 2 mu. So there's a small mistake here. It's a plus here. So this will also become a plus. So we understood the method. Understood the method. So just just write out this method also you should get the very same answer. Okay. So I'm not wasting time doing it. Okay. Is this clear? So all you need to understand is when you have been given such a scenario. It's as good as saying R minus a vector is coplanar to is coplanar to vector B and C. Okay. So this is another way of expressing R minus a BC STP is equal to zero. So this is equivalent to saying R is equal to a plus lambda B plus mu C. So don't be surprised when you see such a equation given to you. Don't misunderstand this as a equation of a line because it resembles very much like a equation of a line. If just this mu C has not had not been there, it would have resembled a equation of a line. Is the idea clear how this works? And this is not there in your NCRT. Okay. Now let us take few mix and match of these concepts that we have learned through problems.