P Y R 



P Y R 



Icenery. In general his piftures are of a fmall fize, and 

 are rather fcarce. He died in 1673, at the age of 52. 



PYNANG, in Botany, a name by which fome authors 

 call the faiifel, or areca-{ree ; a kind of palm, from the cx- 

 prcifed juice of which the drug commonly, but improperly, 

 called Japan -earth is made. 



PYNY, in Geography, a town of Hindooftan, in Coim- 

 betore ; iR miles S. of Daraporum. 



PYONY Wateh. See Water. 



PYRACANTHA, in Botany, a name given by fome 

 authors to the lycium, or box-thorn. 



PYRjEIA, or Pyketiiea, among the Eajlern Nations 

 of Antiquity, were great inclofures uncovered, and dedi- 

 cated to the fun, in which a perpetual fire was kept up in 

 honour of this luminary, which was worfliipped by moil of 

 them. See Ciia.manim. 



PYRALIS, thzjire-fly, a name given by authors to a 

 fuppofed infetl, which they fay is produced in the violent 

 fires of the glafs and metal furnaces. Plin. lib. ii. c. xxxvi. 

 See Lampyris. 



PYRAMID, TO'jfa^i,-, in Geometry, a folid (landing on a 

 fquare, triangular, or polygonal bafis, and terminating at 

 top in a point ; or a body whofe bafe is a regular rcftihnear 

 figure, and whofe fides are plain triangles ; their feveral ver- 

 tices meeting together in one point. 



Euclid defines it a folid figure, confifting of feveral tri- 

 angles whofe bafes are all in the fame plane, and have one 

 common vertex. 



Wolfius defines it a folid, bounded by as many triangles, 

 ADC, D C B, and A D B, terminating in one point D, 

 as the bafe A B C has fides. Plate XI. Geometry, fig. 18. 



The pyramid is faid to be triangular, quadrangular, quln- 

 quangular, &c. according as the bafe is triangular, quadran- 

 gular, &c. The pyramid may be called a fquare, triangu- 

 lar, &c. cone ; or the cone a round pyramid. 



Pyramid, Properties of the. I. All pyramids and cones 

 ftanding on the fame bafe, and having the fame altitude, are 

 demonilrated to be equal. 



2. A triangular pyramid is the third part of a prifm, 

 ftandins; on the fame bafe, and of the fame altitude. 



3. Hence, fince every multangular may be divided into 

 triangulars, every pyramid is the third part of a prifm, 

 ftanding on the fame bafis, and of the fame altitude. 



4. If a pyramid be cut by a plane, ab c, parallel to4ts bafe, 

 ABC, the former plane, or bafe, will be fimilar to the latter. 



5. All pyramids, prifms, cylinders, &c. are in a ratio 

 compounded of their bafes and altitudes : the bafes, there- 

 fore, being equal, they are in proportion to their altitudes ; 

 and the altitudes being equal, they are in proportion to 

 their bafes. 



6. Similar pyramids, prifms, cylinders, cones, &c. are 

 in a triplicate ratio of their homologous fides. 



7. Equal pyramids, &c. reciprocate their bafes and alti- 

 tudes ; i. e. the altitude of the one is to that of the other, 

 as the bafe of this to the bafe of that. 



8. A fphere is equal to a pyramid, whofe bafe is equal 

 to the furfacc, and its height to the radius of the fphere. 



Pyramid, to meafure the furface and folidtly of a. Find 

 the folidity of a prifm that has the fame bafe and height 

 with the given pyramid. And divide this by three ; the 

 quotient will be the folidity of the pyramid. Or, multiply 

 the bafe by the perpendicular height ; and one-third of the 

 produft will be the content. 



Suppofe, V. gr. the folidity of the prifm be found 

 67010328, the folidity of the pyran^d will be thus found 

 72336776. 



Vol. XXIX. 



The furfacc of a pyramid is had, by finding the areas, 

 both of a bafe, ABC, and of the lateral triangles, A CD, 

 C B D, D B A. (See Triangles. ) The fum of thefe ic 

 the area of the pyramid. 



The external furface of a right pyramid, fl;anding on a 

 regular polygonal bafe, is equal to the altitude of one of 

 the triangles which compofe it, multiplied by the whole 

 circumference of the bafe of the pyramid. 



Py'RAMID on a plane, to dejcrihe a. I. Draw the bafe, 

 •0. gr. the triangle ABC (if the pyramid required be tri- 

 angular) ; fo as that the fide A B, luppoied to be turned 

 behind, be not exprefled. 2. On AC and C B, conftruft 

 the triangles ADC and C D B, meeting in any affumed 

 or determined point, v. gr. D ; and draw AD, CD, BD; 

 then will ADBC be a triangular pyramid. 



Pyramid of pajleboard, &c. to conflruB a. Suppofe, 

 1), gr. R triangular pyramid required, i. With the radius 

 A B defcribe an arc BE {fig. 19.) ; and to this arc apply 

 three equal chords, BC, CD, and DE. 2. On CD con- 

 ftruifl an equilateral triangle, DFC, and draw the right 

 lines A D and A C. This palleboard, &c. being cut off 

 by the contour of the figure, what remains within will 

 turn up into a pyramid. 



Pyramid, Truncated. See Truncated. 

 Pyramid, Fi ufium of a. See Frustum. 

 Pyramid, in Archiietlure, denotes a folid, maffive edifice ; 

 which, from a fquare, triangular, or other bafe, rifes dimi- 

 nifliing to a point, or vertex. 



Some derive the word from wupo;, 'wheat, ai'd a^aa, 

 colligo ; pretending that the firll pyramids were built by the 

 patriarch Jofeph, for granaries. But ViUalpandus, with 

 much better reafon, derives the word from vrKp , fire ; be- 

 caufe of their ending in a point like flame. 



Wilkins, converfant with the Coptic tongue, fuggefts 

 (Difl. de Ling. Copt.) another derivation from that lan- 

 guage, in which poure fignifies a king, and mifii, a race or 

 generation ; and he fays, the pyramids were thus called, 

 becaufe they were erefted to preferve the memories of the 

 Egyptian kings and their families ; and that thofe who de- 

 fcended from them had recourfe to thefe pillars in order to 

 prove their pedigree. 



When they are very narrow at bottom, t. e. their bafe 

 very fmall, they are called obeltfks, and needles. 



Pyramids are fometimes erefted to preferve the memory 

 of Angular events, and, fometimes, to tranfmit to pofterity 

 the glory and magnificence of princes ; but, as they are 

 the fymbols of immortality, they are more commonly ufed 

 as funeral monuments 



Such is that of Ceftius at Rome, the maufoleum of this 

 diftinguilhed Roman, who was one of the feven officers 

 called Epulones, and is faid to have lived under Auguftus, 

 repaired in 1673, by Alexander VII. and thofe other 

 celebrated ones of Egypt, as famous for their fize as 

 their antiquity ; and reckoned by the ancients among the 

 wonders of the world, 



Thefe lad are all fquare in their bafes ; and it is a thing 

 that has been frequently propofed, to eftablifh a fixed mea- 

 iure from them, to be thereby tranfmitted to pofterity. 

 See their defcriptions, meafures, &c. in Thevenot, Pietro 

 della Valle, Greaves, Pococke, Shaw, Perry, Maillet, Sa- 

 vary, &c. The pyramids of Egypt, comprehending the 

 great and fmall, are very numerous ; of thefe there are about 

 twenty of the largelt fize. The mofl remarkable are the 

 three pyramids of Memphis, or, as they are now called, of 

 Ghcifa, Geeza, or Gize. The dimenfions of the greateft 

 of thefe have been ditTerently Hated both by ancient and 



I moderB 



