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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Page 2
... Perpendicular to that ( AB ) whereon it ftandeth . Note , When feveral angles meet at the fame point ( as at G ) each particular angle is defcribed by three letters ; whereof the middle letter fheweth the angular point , and the two ...
... Perpendicular to that ( AB ) whereon it ftandeth . Note , When feveral angles meet at the fame point ( as at G ) each particular angle is defcribed by three letters ; whereof the middle letter fheweth the angular point , and the two ...
Page 15
... perpendicular required . For the triangles DFC , EFC are mutually ce - c conftr . quilateral ; d therefore the angle DCF ECF . ed 8. 1 . therefore FC is perpendicular . Which was to be done.e 10. def . The practice of this and the ...
... perpendicular required . For the triangles DFC , EFC are mutually ce - c conftr . quilateral ; d therefore the angle DCF ECF . ed 8. 1 . therefore FC is perpendicular . Which was to be done.e 10. def . The practice of this and the ...
Page 16
... perpendicular BE . Because the angle ABC cto a right ABE , ̄` · and the angles ABD d to a right - ABE , therefore fhall be ABC + ABD e to two right angles + ABE ABE two right an- gles . Which was to be demonftrated . -- Corollaries . 1 ...
... perpendicular BE . Because the angle ABC cto a right ABE , ̄` · and the angles ABD d to a right - ABE , therefore fhall be ABC + ABD e to two right angles + ABE ABE two right an- gles . Which was to be demonftrated . -- Corollaries . 1 ...
Page 18
... perpendicular AD let fall from any point A to the other line CD , fhall fall on that fide the acute is of . For if AC , drawn on the fide of the obtuse an- gle , be a perpendicular , then in the triangle A EC fhall AEC ACE be * greater ...
... perpendicular AD let fall from any point A to the other line CD , fhall fall on that fide the acute is of . For if AC , drawn on the fide of the obtuse an- gle , be a perpendicular , then in the triangle A EC fhall AEC ACE be * greater ...
Page 36
... the point C erect a perpendicular CE meeting with the circumference in E ; and draw BE . a Then is BEq ( BAq ) BCq + CEq . Therefore BAq BCq CEq . Which was to be done . 11 B PRO- 10 6 B BCq - ABq PROBLEM III . 8 36 The first Book of.
... the point C erect a perpendicular CE meeting with the circumference in E ; and draw BE . a Then is BEq ( BAq ) BCq + CEq . Therefore BAq BCq CEq . Which was to be done . 11 B PRO- 10 6 B BCq - ABq PROBLEM III . 8 36 The first Book of.
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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 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 theſe thofe thoſe triangle ABC whence Wherefore whofe whole