Page:Algebra, with Arithmetic and mensuration, from the Sanscrit.djvu/100

 CHAPTER 11. SECTION I. Invocation.'^ 9- Salutation to G an'es'a, resplendent as a blue and spotless lotus; and delighting in the tremulous motion of the dark serpent, which is perpetually- twining within his throat. Numeration. 10 — 11. Names of the places of figures have been assigned for practical use by ancient writers,* increasing regularly' in decuple proportion : namely, unit, ten, hundred, thousand, myriad, hundred thousands, million, ten millions, hundred millions, thousand millions, ten thousand millions, hundred thousand millions, billion, ten billions, hundred billions, thousand billions, ten thousand billions, hundred thousand billions.* ' A reason of this second introductory stanza is, that the foregoing definitions of terms are not properly a part of the treatise itself; nonesuch having been premised by Arya-biiatt'a and other ancient authors to their treatises of arithmetic. Gan. and Mono. ^ According to the Hindus, numeration is of divine origin ; ' the invention cf nine figures (anca), with the device of places to make them suffice for all numbers, being ascribed to the beneficent Creator of the universe,' in Bhascara's Vdsand and its gloss; and in Crishna's commentary on the Vija-garika. Here nine figures are specified ; the place, when none belongs to it, being shown by a blank (sunya) ; which, to obviate mistake, is denoted by a dot or small circle. ' From the right, where the first and lowest number is placed, towards the left hand. Gas. &c. ♦ Sans, ka, daia, sata, sahasra, ayuta, lacsha, prayuta, coti, arbuda, abja or padma, c'/iarva, nic'harva, mahdpadma, sancu,jalad'hi or samudra, antya, mad'hya, par&rd'ha. A passage of the Veda, which is cited by Su'rya-dasa, contains the places of figures. 'Be these the milch kine before me, one, ten, a hundred, a thousand, ten thousand, a hundred thousand, a million Be these milch kine my guides in this world.' Ga'n'esa observes, that numeration has been carried to a greater number of places by Srid'iiara and others ; but adds, that the names are omitted on account of the numerous contradictions and the little utility of tljose designations. The text of the Gaiiita-s/ira or abridgment of Srid'hara does not correspond with this reference : for it exhibits the same eighteen places, and no more. Gari-sdr. § 2—3.)