All Quotes

"Sexy is in the attitude. It's sexy when you are comfortable in your own skin. It doesn't have anything to do with your shape or your physical appearance."

"Time has a way of sorting things out."

"My passion is life. When I do something, I’m super all out there. I cannot single out anything."

"For people to call me out na parang ‘bat ganyan ka?’ I’m not the one telling people: ‘bat ka ordinaryo?."

"I don’t have to justify what I do. I’m only answerable to God and my family"

"Women nowadays are the most empowered ever. We are in this generation that women don’t have to justify themselves. We can do anything we want."

"Women rule!"

"I think what really matters is family in the end."

"I guess my outlet was to dress up and look like this [laughs] and it snowballed into being weirder and bigger."

"I’m a shopper, but I’m a smart shopper, so I go for high-quality products."

"True, the discovery is also claimed for India. The work relied on is the Apastamba-Sulba-Sutra, the date of which is put at least as early as the fifth or fourth century B.C., while it is remarked that the matter of it must have been much older than the book itself ... There is a proposition stating the theorem of Eucl. I. 47 as a fact in general terms, but without proof […] Certain considerations suggest doubts as to whether the proposition had been established by any proof applicable to all cases. Thus Apastamba mentions only seven rational right angle triangles; he had no general rule such as that attributed to Pythagoras for forming any number of rational right-angle triangles; [his words imply] that he knew no other such triangles. […] the theorem is enunciated and used as if it were of general application; there is, however, no sign of any general proof; there is nothing in fact to show that the assumption of its universal truth was founded on anything better than an imperfect induction from a certain number of cases, discovered empirically, of triangles with sides in the ratios of whole numbers in which the property (1) that the square on the longest side is equal to the sum of the squares on the other two was found to be always accompanied by the property (2) that the latter two sides include a right angle."

"Though this is the proposition universally associated by tradition with the name of Pythagoras, no really trustworthy evidence exists that it was actually discovered by him."

"All our Greek texts of the Elements up to a century ago…purport in their titles to be either ‘from the edition of Theon’…or ‘from the lectures of Theon... [Greek commentaries] commonly speak of the writer of the Elements instead of using his name."

"As with the individual, so with the nation dost Thou deal most mercifully. With the breath of Thy love Thou hast called it into existence. Thou didst bless it with wise and prudent founders. Thou hast implanted in the breasts of its citizens a sense of right, a love of justice. Thou hast watched over its beginnings. Thou hast brought it, in a brief space of time, to a height of unparalleled prosperity. Thou hast, when its existence was endangered, either by attacks from without or by dissensions within, filled the hearts of its faithful children with love and devotion, and Thou hast raised from among them valiant men to defend its interests. Thou hast led them to victory, and when Thou didst make them victorious, Thou didst, too, inspire them with mercy and compassion for the vanquished. For all this, Oh Heavenly Father, we return loving thanks."

"Under his careful and prudent administration the diocese has prospered and acquired order and solidity."

"Analysis (bija) is the intellect assisted by the various symbols that has now taken the name algebra (bijaganita)."

"The science of calculations with unknowns is the source of the science of calculations with knowns."

"What the learned calculators (sankhyah) describe as the originator of intelligence, being directed by a wise being (satpurusha) and which alone is the primal cause (bija) of all knowns (vyakta), I venerate that invisible Supreme Being as well as that science of calculation with unknowns […] Since questions can scarcely be solved without the reasoning of algebra—not at all by those of dull perceptions—I shall speak, therefore, of the operations of analysis."

"I bow to Lord Shiva whose Lotus feet are rubbed by the foreheads of the Lotus-born (Brahma) and Krisha, to Him, a mere recollection of whose name is a source of fortune and end of misfortune for gods, demons, and men. (Ganitapada, Aryabhatiyabhashya) I bow to Shambhu, who is the cause of creation and destruction of the universe, (the different parts of ) whose body are the Sun etc., and who is as effulgent as tens of thousands of suns. (Ganitapada, Aryabhatiyabhashya). I bow to God Shiva, the support of the three worlds, who though inconceivable by nature, being mercy incarnate, assumedthe eight forms, viz. The Sun, the Moon, the Ether, Fire, Air, Water, Earth, and the Sacrificer, for the good of the entire world. (Kalakriyapada, Aryabhatiyabhashya)I bow to God Shambhu who bears on His forehead a digit of the moon illumining all directions by its rays, to Him whose feet are adored by the gods and who is a source of all knowledge. (Mahabhaskariya, opening verse)"

"The line which passes through Lanka, Vatsyapura, Avanti, Sthánesvara, and the "abode of the gods" [= Mount Meru = north pole] is the prime meridian [desantara vidhàyani, lit. the prime meridian for longitude differences.]"

"On any day calculate the longitude of the Sun and the Moon for sunrise or sunset without applying the longitude correction, and therefrom find the time (since sunrise or sunset), in ghatis, of rising or setting of the Moon; and having done this, note the corresponding time in ghatis from the water clock. From the difference, knowledgeable astronomers can calculate the local longitude in time.*?"

"I adore that Brahman, also that science of calculation with the unknown, which is the one invisible root-cause of the visible and multiple-qualified universe, also of multitudes of rules of the science of calculation with the known."

"As out of Him is derived this entire universe, visible and endless, so out of algebra follows the whole of arithmetic with its endless varieties (of rules). Therefore, I always make obeisance to Shiva and also to (avyakta) ganita (algebra)."

"Let ‘so much as’ (yavattavat) be put for the value of the unknown quantity, and doing with that precisely what is proposed in the instance [i.e. what is proposed in the following], let two equal sides be carefully completed, adding or subtracting, multiplying or dividing, [as the case may require]. Subtract the unknown quantity of one side from that of the other; and the known number of the one from that of the other side. Then divide the remainder of the known quantity by the [coefficient of the] remaining unknown: the quotient is the distinct value of the unknown quantity."

"A person has 300 rupees and 6 horses; and another person has 10 horses and 100 rupees debt; and the property of the two is equal; and the price of the horses is the same; what then is the value of each?"

"On a plane surface describe a circle of any specified radius with a pair of compasses. Mark on its circumference 360 degrees. Draw the east-to-west and north-to-south lines through its center. These lines will divide the circle into quadrants, which should be taken into consideration in the leftwise manner (i.e. anti-clockwise)."

"The Rsines of any two arcs of a circle are reciprocally multiplied by their Rcosines; the products are then divided by the radius; the sum of the quotients is equal to the Rsine of the sum of the two arcs, and their difference is the Rsine of the difference of the arcs."

"Without the knowledge of upapattis, by merely mastering the calculations (ganita) described here, from the madhyamadhikara (the first chapter of Siddhantashiromani) onwards, of the [motion of the] heavenly bodies, a mathematician will not be respected in the scholarly assemblies; without the upapattis he himself will not be free of doubt…."

"The first known mention of the geometric series is due to Mahavira (850 CE) in his Ganitasarasangraha (ii.93): पदमितगुणहतिगुणितप्रभवस््स्ययाद्णगु धनं तदाद्यूनम।् एकोनगुणविभक्तं गुणसङ्कलितं विजानीयात्॥ which translates to The first term when multiplied by the continued product of the common ratio, taken as many times as the number of terms, gives rise to the gunadhana [the (n+1)th term of the geometric progression]. And it has to be understood that this gunadhana, when diminished by the first term and then divided by the common ratio lessened by one, becomes the sum of the series in the geometric progression."

"The Moon, moving like a cloud in a lower sphere, overtakes the Sun [and obscures its shining disk by its own dark body] hence it arises that the western side of the Sun’s disk is first obscured, and that the eastern side is the last part relieved from the Moon’s dark body: and to some places the Sun is eclipsed and to others is not eclipsed (although he is above the horizon) on account of their different orbits. (1)At the change of the Moon it often so happens that an observer placed at the center of the earth, would find the sun when far from the zenith, obscured by the intervening body of the moon, whilst another observer on the surface of the earth will not at the same time find him to be so obscured, as the moon will appear to him [on the higher elevation] to be depressed from the line of vision extending from his eye to the sun. Hence arises the necessity for the correction of parallax in celestial longitude and parallax in latitude in solar eclipses in consequence of the difference of the distances of the sun and the moon. (2) When the sun and moon are in opposition, the earth’s shadow envelopes the moon in darkness. As the moon is actually enveloped in darkness, and as the earth’s shadow and the moon which enters it, are at the same distance from the earth, there is therefore no call for the correction of the parallax in a lunar eclipse. (3)"

"As the moon moving eastward enters the dark shadow of the earth: therefore its eastern side is first of all involved in obscurity, and its western is the last portion of its disc which emerges from darkness as it advances in its course. (4) As the sun is a body of vast size, and the earth insignificantly small in comparison: the shadow made by the sun from the earth is therefore of a conical form terminating in a sharp point. It extends to a distance considerably beyond that of the moon’s orbit. (5)"

"The length of the earth’s shadow, and its breadth at the part traversed by the moon, may be easily found by proportion. In the lunar eclipse the earth’s shadow is northwards or southwards of the moon when its latitude is south or north. Hence the latitude of the moon is here to be supposed inverse (i.e. it is to be marked reversely in the projection to find the center of the earth’s shadow from the moon.) (6)"

"If the earth were supported by any material substance or living creature, then that would require a second supporter, and for that second a third would be required. Here we have the absurdity of an interminable series. If the last of the series be supposed to remain firm by its own inherent power, then why may not the same power be supposed to exist in the first, that is in the Earth? For is not the Earth one of the forms of the eight-fold divinity i.e. of Shiva? (Goladhyaya, III.4)"

"The property of attraction is inherent in the Earth. By this property the Earth attracts any unsupported heavy thing towards it: The thing appears to be falling [but it is in a state of being drawn to the Earth]. The ethereal expanse being equally outspread all around, where can the Earth fall? (Goladhyaya III.6)"

"As the one-hundredth part of the circumference of a circle is (scarcely different from) a plane, and as the Earth is an excessively large body, and a man exceedingly small (in comparison), the whole visible portion of the Earth consequently appears to a man on its surface to be perfectly plane."

"From a bunch of lotuses, one third is offered to Lord Shiva, one fifth to Lord Vishnu, one sixth to the sun, one fourth to the goddess. The remaining six are offered to the Guru. Find quickly the number of lotuses in the bunch."

"Arjuna became furious in the war and in order to kill Karna, picked up some arrows. With half the arrows, he destroyed all of Karna’s arrows. He killed all of Karna’s horses with four times the square root of the arrows. He destroyed the spear with six arrows. He used one arrow each to destroy the top of the chariot, the flag, and the bow of Karna. Finally he cut off Karna’s head with another arrow. How many arrows did Arjuna discharge?"

"There is no change in infinite (khahara) figure if something is added to or subtracted from it. It is like: there is no change in the infinite Lord Vishnu due to the dissolution or creation of abounding living beings."

"In a triangle or a polygon, it is impossible for one side to be greater than the sum of the other sides. It is daring for anyone to say that such a thing is possible. If an idiot says that there is a quadrilateral of sides 2, 6, 3, 12 or a triangle with sides 3, 6, 9, explain to him that they don’t exist."

"The earth attracts inert bodies in space towards itself. The attracted body appears to fall down on the earth. Since the space is homogeneous, where will the earth fall?"

"On the subject of demonstrations, it is to be remarked that the Hindu mathematicians proved propositions both algebraically and geometrically: as is particularly noticed by Bhaskara himself, towards the close of his algebra, where he gives both modes of proof of a remarkable method for the solution of indeterminate problems, which involve a factum of two unknown quantities."

"Bhaskara […] does not pretend himself to be the inventor, he assumes no character but that of a compiler."

"Almost any trouble and expense would be compensated by the possession of the three copious treatises on algebra from which Bhaskara declares he extracted his Bijaganita, and which in this part of India are supposed to be entirely lost."

"Reuben Burrow […] says, he was told by a pundit, that some time ago there were other treatises of algebra."

"This method is supreme above all praise; it is certainly the finest thing accomplished in number theory before Lagrange."

"O! tender girl, out of the swans in a certain lake, ten times the square root of their number went away to Manasarovara when the rainy season arrived, one eighth of that number went away to the Sthala Padmini forest. Three pairs of swans remained in the tank, sporting in the water. What is the total number of swans?"

"In His time, I God's time."

"The science of numbers is used in all transactions whether earthly or Vedic, meditation or business, in the science of love, in the art of cooking, in economics and statecraft, in music and medicine, in theatre, architecture and all such things. (9-10) In prosody, in poetics and poetry, in logic, grammar and such like, in the presentation of the qualities of various arts, mathematics is held in esteem. For the movements of the sun and stars, for eclipses and planetary motion, for the three significant questions and the course of the moon, for all these connections it is used (11-12). The number, diameter and perimeter of islands, of oceans and mountains, for the dimensions of rows of buildings of the earth’s inhabitants, of the space between the worlds, of the world of light, for the worlds of devas, for the dimensions of the dwellers in hell; for measurements of all sort and voluminous evidence, all these are made out by means of computation (13- 14). The organization of living beings, the length of their lives, their eight attributes and other similar things, their travel and cohabitation and such other things, all depend on mathematics. What more can be said? All there is in the three worlds, moving or unmoving, all that cannot be described without mathematics (15-16)."

"The first known mention of the geometric series is due to Mahavira (850 CE) in his Ganitasarasangraha (ii.93): पदमितगुणहतिगुणितप्रभवस््स्ययाद्णगु धनं तदाद्यूनम।् एकोनगुणविभक्तं गुणसङ्कलितं विजानीयात्॥ which translates to The first term when multiplied by the continued product of the common ratio, taken as many times as the number of terms, gives rise to the gunadhana [the (n+1)th term of the geometric progression]. And it has to be understood that this gunadhana, when diminished by the first term and then divided by the common ratio lessened by one, becomes the sum of the series in the geometric progression."

"The sum of an infinite [anantya] series, whose later terms (after the first) are got by dividing the preceding one by the same divisor everywhere, is equal to the first term multiplied by the common divisor, and divided by one less than the common divisor."