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 |
Im Buch
Ergebnisse 1-5 von 23
Seite 63
... Likewise a 32. t . the angle EDC = 2 DAC . Therefore in the first b 5. 1 . cafe the whole angle c BDC 2 BAC . and in c 2. ax . the third cafe the d remaining angle BDC = 2 d 20. aš . BAC . Which was to be dem . PROP . XXI . F D E E In a ...
... Likewise a 32. t . the angle EDC = 2 DAC . Therefore in the first b 5. 1 . cafe the whole angle c BDC 2 BAC . and in c 2. ax . the third cafe the d remaining angle BDC = 2 d 20. aš . BAC . Which was to be dem . PROP . XXI . F D E E In a ...
Seite 95
... is equal to F. Likewise the number of parts in BG is equal to the number of parts in EH . Therefore the number of parts in AB → BG is equal to the number of parts in DE → EH . 2 2. ax . a byp b 205 . 62.5 EUCLIDE's Elements .
... is equal to F. Likewise the number of parts in BG is equal to the number of parts in EH . Therefore the number of parts in AB → BG is equal to the number of parts in DE → EH . 2 2. ax . a byp b 205 . 62.5 EUCLIDE's Elements .
Seite 101
... likewise a because E. F :: C. D. if I ,, M , b then is H likewife ,, L . c wherefore A. B :: C. D. Which was to be dem . c 6. def . s . Schol . Proportions that are one and the fame to the fame proportions , are the fame betwixt them ...
... likewise a because E. F :: C. D. if I ,, M , b then is H likewife ,, L . c wherefore A. B :: C. D. Which was to be dem . c 6. def . s . Schol . Proportions that are one and the fame to the fame proportions , are the fame betwixt them ...
Seite 108
... likewise I , = , M. and fo à confequently A. C : D. F. Which was to be a 6. def.5.demonftrated . * 22. & 23 . def . 1 . If there be more magnitudes than three , this way of demonftration holds good in them alfo . Coroll . From hence it ...
... likewise I , = , M. and fo à confequently A. C : D. F. Which was to be a 6. def.5.demonftrated . * 22. & 23 . def . 1 . If there be more magnitudes than three , this way of demonftration holds good in them alfo . Coroll . From hence it ...
Seite 139
... likewise the sector BDI , FHP ; m thence fhall be the sector m 6.def.s BDC . FHG :: the arch BC . FG . Which was to be demonftrated . 1 Coroll . 1. Hence , As fector is to fector , fo is angle to 11. 5 . angle . 2. The angle BDC in the ...
... likewise the sector BDI , FHP ; m thence fhall be the sector m 6.def.s BDC . FHG :: the arch BC . FG . Which was to be demonftrated . 1 Coroll . 1. Hence , As fector is to fector , fo is angle to 11. 5 . angle . 2. The angle BDC in the ...
Andere Ausgaben - Alle anzeigen
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.