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 páginas |
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Página 7
... remaining will be equal . 4. If to unequal things you add equal things , the wholes will be unequal . 5. If from unequal things you take away equal things , the remainders will be unequal . 6. Things which are double to the fame third ...
... remaining will be equal . 4. If to unequal things you add equal things , the wholes will be unequal . 5. If from unequal things you take away equal things , the remainders will be unequal . 6. Things which are double to the fame third ...
Página 11
... remaining angles B , C , fhall be equal to the remaining angles E , F , each to each , under which the equal fides are fubtended . DF . b 14. as . If the point D'be applied to the point A , and the right line DE plac'd upon the right ...
... remaining angles B , C , fhall be equal to the remaining angles E , F , each to each , under which the equal fides are fubtended . DF . b 14. as . If the point D'be applied to the point A , and the right line DE plac'd upon the right ...
Página 26
... remaining angle of the one equal to the remaining angle of the other . In like man- ner , if two triangles have one angle of the one equal to one of the other , then is the fum of the remaining angles of the one triangle equal to the ...
... remaining angle of the one equal to the remaining angle of the other . In like man- ner , if two triangles have one angle of the one equal to one of the other , then is the fum of the remaining angles of the one triangle equal to the ...
Página 27
... remaining angles , which make up the angles of the figure , will make twice as many right angles , bating four , as there are fides of the figure . Which was to be dem . Coroll . Hence , All right - lined figures of the fame fpecies ...
... remaining angles , which make up the angles of the figure , will make twice as many right angles , bating four , as there are fides of the figure . Which was to be dem . Coroll . Hence , All right - lined figures of the fame fpecies ...
Página 61
... remaining angle without the circumference DAI is lefs than any right - lined angle . 1. From the center B to any point F in the right line AC , draw the right line BF . The fide BF fubtending the right angle BAF is a greater a 19. 1 ...
... remaining angle without the circumference DAI is lefs than any right - lined angle . 1. From the center B to any point F in the right line AC , draw the right line BF . The fide BF fubtending the right angle BAF is a greater a 19. 1 ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 2 - The radius of a circle is a right line drawn from the centre to the circumference.
Página 1 - Bounds) of a Line, are Points. IV. A Right Line, is that which lietb evenly between its Points.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.