Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. With Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of IndivisiblesW. Redmayne, 1714 - 520 Seiten |
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Seite 1
... Superficies are lines . VII . A plain Superficies is that which lies equally betwixt its lines . VIII . A plain Angle is the inclination of two lines the one to the other , the one touching the other in the fame plain , yet not lying in ...
... Superficies are lines . VII . A plain Superficies is that which lies equally betwixt its lines . VIII . A plain Angle is the inclination of two lines the one to the other , the one touching the other in the fame plain , yet not lying in ...
Seite 267
... Superficies . B ཡ H EGKB III . A right line AB is perpendicular to a Plane CD , when it makes right angles ABD , ABE , ABF , with all the right lines BD , BE , BF , - that touch it , and are drawn in the faid Plane . IV . A Plane AB ...
... Superficies . B ཡ H EGKB III . A right line AB is perpendicular to a Plane CD , when it makes right angles ABD , ABE , ABF , with all the right lines BD , BE , BF , - that touch it , and are drawn in the faid Plane . IV . A Plane AB ...
Seite 341
... superficies of a dodecaedron . € 17. 3 . Which was to be dem . Draw LI , LH , LK ; then HK x LM f is 2 triang . LHK . therefore 30 HK x LM g HLK = 20 HIK b to the fuperficies of an Icofaedron . Which was to be dem . f 41. I. g 815. 5 ...
... superficies of a dodecaedron . € 17. 3 . Which was to be dem . Draw LI , LH , LK ; then HK x LM f is 2 triang . LHK . therefore 30 HK x LM g HLK = 20 HIK b to the fuperficies of an Icofaedron . Which was to be dem . f 41. I. g 815. 5 ...
Seite 361
... Superficies , and into circular Theoremes , which Order he hath also obferved in the Definitions and Suppofitions of this Book . Moreover , he ufeth a certain way of inftructing , which proceeds not by Com- pofition , but by Refolution ...
... Superficies , and into circular Theoremes , which Order he hath also obferved in the Definitions and Suppofitions of this Book . Moreover , he ufeth a certain way of inftructing , which proceeds not by Com- pofition , but by Refolution ...
Seite 505
... Superficies of the circle confifts of in- finitely many concentric Peripheries . Which method of indivifibles , ( now first of all known to me ) feems no lefs evident ( nay more evident ) and perhaps lefs fallacious than that wherein ...
... Superficies of the circle confifts of in- finitely many concentric Peripheries . Which method of indivifibles , ( now first of all known to me ) feems no lefs evident ( nay more evident ) and perhaps lefs fallacious than that wherein ...
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Häufige Begriffe und Wortgruppen
ABC is given ABCD abfurd alfo given alſo altitude angle ABC angle BAC bafe baſe becauſe bifect circle commenfurable compounded Cone confequently conftr Coroll cube defcribed Demonftr diameter Dodecaedron drawn equilateral faid fame fecond feeing fegment fhall fide figure firft fome Forafmuch fore fphere fquare number fubtended fuch fuperficies fuppofed given by kind given by magnitude given by pofition given magnitude given reafon greater hath Icofaedron infcribed interfection leaft lefs likewife meaſure medial oppofite parallel parallelepipedon parallelogram pentagone perpendicular plane prifms PROP proportion pyramides rectangle refidual line right angles right line AB right line BC right line given Schol Scholium ſhall thefe thofe thoſe triangle ABC whence Wherefore whofe whole
Beliebte Passagen
Seite 26 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 406 - ... which, when produced, the perpendicular falls, and the straight line intercepted, without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn...
Seite 269 - A fphere is a folid figure defcribed by the revolution of a i'emicircle about its diameter, which remains unmoved. XV. The axis of a fphere is the fixed ftraight line about which the femicircle revolves. XVI. The centre of a fphere is the fame with that of the femicircle. XVII. The diameter of a fphere is any ftraight line which pafles through the centre, and is terminated both ways by the fuperficies of the fphere.
Seite 2 - The radius of a circle is a right line drawn from the centre to the circumference.
Seite 1 - Bounds) of a Line, are Points. IV. A Right Line, is that which lietb evenly between its Points.
Seite 269 - ... be less than the other side, an obtuse angled ; and if greater, an acute angled cone. XIX. The axis of a cone is the fixed straight line about which the triangle revolves. XX. The base of a cone is the circle described by that side containing the right angle which revolves. XXI. A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed.
Seite 26 - ... the fum of the remaining angles of the one triangle equal to the fum of the remaining angles of the other. 3 . If one angle in a triangle be right, the other two are equal to a right-angle.
Seite 76 - ... the angular points of the figure about which it is defcribed, each thro' each. III. A rectilineal figure is faid to be infcribed in a circle, when all the angles of the infcribed figure are upon the circumference of the circle.
Seite 77 - ... touch the circumference of the circle. IV A right-lined figure is faid to be defcribed about a circle, when all the fides of the figure which is circumfcribed touch the periphery of the circle V.
Seite 269 - Right Lines that touch one another, and are •not in the fame Superficies: Or, a folid Angle is that which is contained under more than two plane Angles which are not in the fame Superficies, but being all at one Point.