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 14
... given AB . Upon the line given AB a erect an equilateral triangle ABC ; and b bifect the angle C with the right line CD . That line fhall also bisect the Bline given AB . For ACc BC , and the fide CD is common , and the angle ACDC - BCD ...
... given AB . Upon the line given AB a erect an equilateral triangle ABC ; and b bifect the angle C with the right line CD . That line fhall also bisect the Bline given AB . For ACc BC , and the fide CD is common , and the angle ACDC - BCD ...
Seite 21
... given any ways ; b make AGCD ; upon AG craife a trian- b.3 . r . gle equilateral to the former CDF , fo that AH be c ... also have the bafe BC greater than the bafe EP . a Let the angle EDG be made equal to A , a 23. 1 . and the fide DG ...
... given any ways ; b make AGCD ; upon AG craife a trian- b.3 . r . gle equilateral to the former CDF , fo that AH be c ... also have the bafe BC greater than the bafe EP . a Let the angle EDG be made equal to A , a 23. 1 . and the fide DG ...
Seite 25
... given any ways , then because AB , EF are parallel , will be the angle AGI a - EHI . also because CD and EF are pa- a 29.1 . rallel , will be the angle EHI a - DIG . b The e - b 1. ax . fore the angle AGI DIG . c whence AB and CD are ...
... given any ways , then because AB , EF are parallel , will be the angle AGI a - EHI . also because CD and EF are pa- a 29.1 . rallel , will be the angle EHI a - DIG . b The e - b 1. ax . fore the angle AGI DIG . c whence AB and CD are ...
Seite 81
... given EABCD to inferibe a Square ABCD . a Draw the diameters a īta ka AC , BD cutting each other at right angles in ... also right - angled . It is equilateral becaule FGd = HId - DBe CAd FHdd 34. t . GI . Wherefore FHIG is a f fquare ...
... given EABCD to inferibe a Square ABCD . a Draw the diameters a īta ka AC , BD cutting each other at right angles in ... also right - angled . It is equilateral becaule FGd = HId - DBe CAd FHdd 34. t . GI . Wherefore FHIG is a f fquare ...
Seite 133
... given ABEDC to defcribe another figure P like and alike fituate , which also shall equal to another right - lined figure given F. a Make the rectangle ALABEDC ; b also a 45. 1 . upon BL make the rectangle BM - F ; betwixt b 44. I. AB ...
... given ABEDC to defcribe another figure P like and alike fituate , which also shall equal to another right - lined figure given F. a Make the rectangle ALABEDC ; b also a 45. 1 . upon BL make the rectangle BM - F ; betwixt b 44. I. AB ...
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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.