The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfthF. Wingrave, 1804 |
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Página 189
... fphere . XVIII . A Cone is a folid figure described by the revolution of a right angled triangle about one of the fides containing the right angle , which fide remains fixed . Book XI . If the fixed fide be equal to OF EUCLID . 189.
... fphere . XVIII . A Cone is a folid figure described by the revolution of a right angled triangle about one of the fides containing the right angle , which fide remains fixed . Book XI . If the fixed fide be equal to OF EUCLID . 189.
Página 190
... Cone is called a right angled Cone ; if it be lefs than the other fide , an obtuse angled , and if greater , an acute angled Cone . XIX . The axis of a Cone is the fixed ftraight line about which the triangle revolves . XX . The bafe of ...
... Cone is called a right angled Cone ; if it be lefs than the other fide , an obtuse angled , and if greater , an acute angled Cone . XIX . The axis of a Cone is the fixed ftraight line about which the triangle revolves . XX . The bafe of ...
Página 261
... cone is the third part of a cylinder which has the fame bafe , and is of an equal altitude with it . Let a cone have the fame base with a cylinder , viz . the circle ABCD , and the fame altitude . the cone is the third part of the ...
... cone is the third part of a cylinder which has the fame bafe , and is of an equal altitude with it . Let a cone have the fame base with a cylinder , viz . the circle ABCD , and the fame altitude . the cone is the third part of the ...
Página 262
... . fegments of the cylinder which together are lefs than the excess of the cylinder above the triple of the cone . let them be those upon the As was fhewn in Prop . 2. of this Book . H 7.12 . fegments of the circle AE , EB 262 ELEMENTS THE.
... . fegments of the cylinder which together are lefs than the excess of the cylinder above the triple of the cone . let them be those upon the As was fhewn in Prop . 2. of this Book . H 7.12 . fegments of the circle AE , EB 262 ELEMENTS THE.
Página 263
... cone , of which the base is the circle ABCD . but it is alfo lefs , for the pyramid is contained within the cone ; which is impoffible . Nor can the cylinder be less than the triple of the cone . let it be lefs if poffible . therefore ...
... cone , of which the base is the circle ABCD . but it is alfo lefs , for the pyramid is contained within the cone ; which is impoffible . Nor can the cylinder be less than the triple of the cone . let it be lefs if poffible . therefore ...
Términos y frases comunes
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone conſtruction cylinder defcribed demonſtrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fecond fegment fhall fhewn fides fides BA fimilar fince firft firſt folid angle fore fquare fquare of AC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular plane angles PROP Propofition pyramid rectangle contained rectilineal figure right angles ſame ſhall ſpace ſphere ſquare ſtraight line AB THEOR theſe thro tiple triangle ABC wherefore
Pasajes populares
Página 157 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.
Página 24 - ... be equal, each to each ; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, ECA equal to the angles DEF, EFD, viz.
Página 45 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Página 163 - 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 81 - ELF. Join BC, EF ; and because the circles ABC, DEF are equal, the straight lines drawn from their centres are equal: therefore the two sides BG, GC, are equal to the two EH, HF ; and the angle at G is equal to the angle at H ; therefore the base BC is equal (4.
Página 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Página 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.