# Pappus Sentence Examples

**Pappus**quotes from three books of Mechanics and from a work called Barulcus, both by Hero.- Halma) has preserved a fragment, and to which
**Pappus**also refers. **Pappus**, in his Collections, treats of its history, and gives two methods by which it can be generated.- Any plane section of the screw (plectoidal of
**Pappus**) surface so obtained is the quadratrix. - He continued his studies in Strassburg, under the professor of Hebrew, Johannes
**Pappus**(1549-1610), a zealous Lutheran, the crown of whose life's work was the forcible suppression of Calvinistic preaching and worship in the city, and who had great influence over him. - His only extant work is a short treatise (with a commentary by
**Pappus**) On the Magnitudes and Distances of the Sun and Moon. - (iii) Solids of revolution also form a special class, which can be conveniently treated by the two theorems of
**Pappus**(§ 33). - These theorems were discovered by
**Pappus**of Alexandria (c. A.D. - Halley added in his edition (1710) a restoration of Book viii., in which he was guided by the fact that
**Pappus**gives lemmas "to the seventh and eighth books" under that one heading, as well as by the statement of Apollonius himself that the use of the seventh book was illustrated by the problems solved in the eighth. - The other treatises of Apollonius mentioned by
**Pappus**are - 1st, Aayov alroropii, Cutting off a Ratio; 2nd, Xcopiov a7rorop, Cutting off an Area; 3rd, Ocwpui j Av i Tog, Determinate Section; 4th, 'Eiraci)aL, Tangencies; 5th, 11-€1,o-as, Inclinations; 6th, Tinrot bri ret50t, Plane Loci. - Each of these was divided into two books, and, with the Data, the Porisms and Surface-Loci of Euclid and the Conics of Apollonius were, according to
**Pappus**, included in the body of the ancient analysis. **Pappus**gives somewhat full particulars of the propositions, and restorations were attempted by P. Fermat (Ouvres, i., 1891, pp. 3-51), F.**PAPPUS**OF ALEXANDRIA, Greek geometer, flourished about the end of the 3rd century A.D.- In this respect the fate of
**Pappus**strikingly resembles that of Diophantus. - In his Collection,
**Pappus**gives no indication of the date of the authors whose treatises he makes use of, or of the time at which he himself wrote. - Suidas says also that
**Pappus**wrote a commentary upon the same work of Ptolemy. - 284-305), that
**Pappus**wrote during that period; and in the absence of any other testimony it seems best to accept the date indicated by the scholiast. - The great work of
**Pappus**, in eight books and entitled 6vvayw'y or Collection, we possess only in an incomplete form, the first book being lost, and the rest having suffered considerably. - Suidas enumerates other works of
**Pappus**as follows: XWpoypacliia obcov i Gepck'iJ, Eis TA 740'6apa Ot13Xia IIToXEµaiov y y6X'Yfs 157r6Avfµa, lroTa/.20US Tob Ev Ats15p, OPECpoKptrtK&. **Pappus**himself refers to another commentary of his own on the 'Avfi ojµµa of Diodorus, of whom nothing is known.- These discoveries form, in fact, a text upon which
**Pappus**enlarges discursively. **Pappus**gives several solutions of this problem, including a method of making successive approximations to the solution, the significance of which he apparently failed to appreciate; he adds his own solution of the more general problem of finding geometrically the side of a cube whose content is in any given ratio to that of a given one.- This serves as an introduction to a general theory of means, of which
**Pappus**distinguishes ten kinds, and gives a table representing examples of each in whole numbers. **Pappus**turns then to a consideration of certain properties of Archimedes's spiral, the conchoid of Nicomedes (already mentioned in book i.- Proposition 30 describes the construction of a curve of double curvature called by
**Pappus**the helix on a sphere; it is described by a point moving uniformly along the arc of a great circle, which itself turns about its diameter uniformly, the point describing a quadrant and the great circle a complete revolution in the same time. - Incidentally
**Pappus**describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere. **Pappus**then enumerates works of Euclid, Apollonius, Aristaeus and Eratosthenes, thirty-three books in all, the substance of which he intends to give, with the lemmas necessary for their elucidation.- In the same preface is included (a) the famous problem known by
**Pappus's**name, often enunciated thus: Having given a number of straight lines, to find the geometric locus of a point such that the lengths of the perpendiculars upon, or (more generally) the lines drawn from it obliquely at given inclinations to, the given lines satisfy the condition that the product of certain of them may bear a constant ratio to the product of the remaining ones; (**Pappus**does not express it in this form but by means of composition of ratios, saying that if the ratio is given which is compounded of the ratios of pairs - one of one set and one of another - of the lines so drawn, and of the ratio of the odd one, if any, to a given straight line, the point will lie on a curve given in position), (b) the theorems which were rediscovered by and named after Paul Guldin, but appear to have been discovered by**Pappus**himself. - (4) Der Sammlung des
**Pappus**von Alexandrien siebentes and achtes Buch griechisch and deutsch, published by C. I. - The Geography is a meagre sketch, based mainly on the Chorography of
**Pappus**of Alexandria (in the end of the 4th century), and indirectly on the work of Ptolemy. - Another group of polyhedra are termed the " Archimedean solids," named after Archimedes, who, according to
**Pappus**, invented them. - In mathematics he wrote two books On means (IIEpL, Ueuoty) Twp) which are lost, but appear, from a remark of
**Pappus**, to have dealt with " loci with reference to means." - He devised a mechanical construction for two mean proportionals, reproduced by
**Pappus**and Eutocius (Comm. - On the authority of the two great commentators
**Pappus**and Proclus, Euclid wrote four books on conics, but the originals are now lost, and all we have is chiefly to be found in the works of Apollonius of Perga. **Pappus**in his commentary on Apollonius states that these names were given in virtue of the above relations; but according to Eutocius the curves were named the parabola, ellipse or hyperbola, according as the angle of the cone was equal to, less than, or greater than a right angle.- The focus of the parabola was discovered by
**Pappus**, who also introduced the notion of the directrix. - The limb of the calyx may appear as a rim, as in some Umbelliferae; or as
**pappus**, in Compositae and Valeriana. - - Feathery
**pappus**attached to the fruit of Groundsel (Senecio vulgaris). - This
**pappus**is either simple (pilose) or feathery (plumose).