The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth |
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Resultat 1-5 av 6
Side 254
ABC to the base DEF , so are the two prisms in the pyramid ABCG to the two
prisms in the pyramid DEFH ; and so are the ... may be shewn of the prisms made
by dividing the pyramids AKLO and DPRS , and of all made by the same number
of ...
ABC to the base DEF , so are the two prisms in the pyramid ABCG to the two
prisms in the pyramid DEFH ; and so are the ... may be shewn of the prisms made
by dividing the pyramids AKLO and DPRS , and of all made by the same number
of ...
Side 255
therefore the base ABC is not to the base DEF , as the pyramid Book XII . ABCG
to any solid which is less than the pyramid DEFH . in the fame manner it may be
demonstrated , that the base DEF is not to the base ABC , as the pyramid DEFH
to ...
therefore the base ABC is not to the base DEF , as the pyramid Book XII . ABCG
to any solid which is less than the pyramid DEFH . in the fame manner it may be
demonstrated , that the base DEF is not to the base ABC , as the pyramid DEFH
to ...
Side 256
Let the pyramids which have the polygons ABCDE , FGHKL for their bases , and
their vertices in the points M , N , be of the fame altitude . as the base ABCDE to
the base FGHKL , so is the pyramid ABCDEM to the pyramid FGHKLN . Divide
the ...
Let the pyramids which have the polygons ABCDE , FGHKL for their bases , and
their vertices in the points M , N , be of the fame altitude . as the base ABCDE to
the base FGHKL , so is the pyramid ABCDEM to the pyramid FGHKLN . Divide
the ...
Side 257
the base FGHKL , so the pyramid ABCDEM to the pyramid Book XII . FGHKLN .
Therefore pyramids , & c . Q. E. D. PROP . VII . THEOR VERY prism having a
triangular base may be divided into three pyramids that have triangular bases ,
and ...
the base FGHKL , so the pyramid ABCDEM to the pyramid Book XII . FGHKLN .
Therefore pyramids , & c . Q. E. D. PROP . VII . THEOR VERY prism having a
triangular base may be divided into three pyramids that have triangular bases ,
and ...
Side 269
6 . the base is the triangle AKQ , and vertex L , is similar to the pyramid the base
of which is the triangle EMS , and vertex ... B. II . by the same number of similar
planes . but similar pyramids which have triangular bases have to one another
the ...
6 . the base is the triangle AKQ , and vertex L , is similar to the pyramid the base
of which is the triangle EMS , and vertex ... B. II . by the same number of similar
planes . but similar pyramids which have triangular bases have to one another
the ...
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added alſo altitude angle ABC angle BAC baſe becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſm produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Side 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.
Side 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.
Side 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 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.
Side 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.