Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. With Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles |
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... Second , thirteenth , and very few in the seventh , eighth , and ninth Book , in which it feem'd not worth my while to deviate in any particular from him . There- fore I am not without good hopes that as to this part I bave in fome ...
... Second , thirteenth , and very few in the seventh , eighth , and ninth Book , in which it feem'd not worth my while to deviate in any particular from him . There- fore I am not without good hopes that as to this part I bave in fome ...
Page 38
... NK a = LQ After the fame manner any rectangles equila- teral one to another , are demonftrated alfo to be equal . The End of the firft Book . THE : THE SECOND BOOK OF EUCLIDE's ELEMENTS . B Definitions 38 The firft Book of , & c .
... NK a = LQ After the fame manner any rectangles equila- teral one to another , are demonftrated alfo to be equal . The End of the firft Book . THE : THE SECOND BOOK OF EUCLIDE's ELEMENTS . B Definitions 38 The firft Book of , & c .
Page 39
... SECOND BOOK OF EUCLIDE's ELEMENTS . B Definitions . A I. E D Very right - angled Parallelogram AB CD is faid to be contained under two right lines AB , AD compre- hending a right angle , Therefore when you meet with fuch as thefe , the ...
... SECOND BOOK OF EUCLIDE's ELEMENTS . B Definitions . A I. E D Very right - angled Parallelogram AB CD is faid to be contained under two right lines AB , AD compre- hending a right angle , Therefore when you meet with fuch as thefe , the ...
Page 42
... . Therefore 29.def . AG , GD are rectangles under AC , CB . where- 19.dx.fore the whole fquare AD kACq CBq → 2 ACB . Which was to be dem . 8 34. I. Coroll Coroll . . Hence it appears that the Parallelograms which 42 The Second Book of.
... . Therefore 29.def . AG , GD are rectangles under AC , CB . where- 19.dx.fore the whole fquare AD kACq CBq → 2 ACB . Which was to be dem . 8 34. I. Coroll Coroll . . Hence it appears that the Parallelograms which 42 The Second Book of.
Page 48
... H. Then fhall be CHq * MLA . For let GH be drawn . DCFdGFq- GCqe Which was to be done . Then is Ac = DB c HCq = ML The End of the fecond Book , ין THE THE THIRD BOOK O F EUCLIDE'S ELEMENTS . B AG The Second Book of , & c .
... H. Then fhall be CHq * MLA . For let GH be drawn . DCFdGFq- GCqe Which was to be done . Then is Ac = DB c HCq = ML The End of the fecond Book , ין THE THE THIRD BOOK O F EUCLIDE'S ELEMENTS . B AG The Second Book of , & c .
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Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 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.
Page 2 - The radius of a circle is a right line drawn from the centre to the circumference.
Page 1 - Bounds) of a Line, are Points. IV. A Right Line, is that which lietb evenly between its Points.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.