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 143
... plane , and folid numbers are they , which have their fides proportional : Namely , not all the fides , but fome . " XXII . A perfect number is that which is equal to all its aliquot parts . As 6 and 28. But a number that is less than ...
... plane , and folid numbers are they , which have their fides proportional : Namely , not all the fides , but fome . " XXII . A perfect number is that which is equal to all its aliquot parts . As 6 and 28. But a number that is less than ...
Página 144
... plane , folid , fquare , or cube number . 8. If one number measures another , that number by which it measures fhall measure the same by the units that are in the number measuring , that is by the number itself that measures . 9. If a ...
... plane , folid , fquare , or cube number . 8. If one number measures another , that number by which it measures fhall measure the same by the units that are in the number measuring , that is by the number itself that measures . 9. If a ...
Página 167
... Plane numbers CD , ED , 18 . EF , are in that propor- tion to one another which is compofed of their fides . For because CD . ED a :: C.E ; a and ED . EF :: a 17.7 . D CD CD D. F. & EF b = 214 ED cthen shall be thepro- b 20.def E CII ...
... Plane numbers CD , ED , 18 . EF , are in that propor- tion to one another which is compofed of their fides . For because CD . ED a :: C.E ; a and ED . EF :: a 17.7 . D CD CD D. F. & EF b = 214 ED cthen shall be thepro- b 20.def E CII ...
Página 172
... plane num- bers CD and EF there is one mean proportional number DE : And the plane CD is to the plane EF in double proportion of that which the fide C has to the homologous fide ( or of like proportion ) E. * * 21.def.7 • fore by ...
... plane num- bers CD and EF there is one mean proportional number DE : And the plane CD is to the plane EF in double proportion of that which the fide C has to the homologous fide ( or of like proportion ) E. * * 21.def.7 • fore by ...
Página 173
... plane numbers . a Take D and E the leaft in the proportion of A a 35. 7 . to C , or C to B. then D measures A ... plane numbers . But because d 16.def.7 . EFc = Cc = DG , e fhall D. E :: F. G. and alter- e 19. 7 . nately f21 . def.7 ...
... plane numbers . a Take D and E the leaft in the proportion of A a 35. 7 . to C , or C to B. then D measures A ... plane numbers . But because d 16.def.7 . EFc = Cc = DG , e fhall D. E :: F. G. and alter- e 19. 7 . nately f21 . def.7 ...
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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.