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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Side 243
IF F there be two triangular prisms of the fame altitude , the base of one of which
is a parallelogram , and the base of the ... for its base ; if the parallelogram AF be
double of the triangle GHK , the prism ABCDEF is equal to the prism GHKLMN .
IF F there be two triangular prisms of the fame altitude , the base of one of which
is a parallelogram , and the base of the ... for its base ; if the parallelogram AF be
double of the triangle GHK , the prism ABCDEF is equal to the prism GHKLMN .
Side 251
these prisms are equal to one another ; therefore the prism having Book XII . the
parallelogram EBFG for its base , and the straight line KH 1. 40. II . opposite to it ,
is equal to the prism having the triangle GFC for its base , and the triangle HKL ...
these prisms are equal to one another ; therefore the prism having Book XII . the
parallelogram EBFG for its base , and the straight line KH 1. 40. II . opposite to it ,
is equal to the prism having the triangle GFC for its base , and the triangle HKL ...
Side 253
ABC to the triangle DEF , fo is the prism having the triangle LXC for its base , and
OMN the triangle opposite to it , to the prism of which the base is the triangle RVF
, and the opposite triangle STY . and because the two prisms in the pyramid ...
ABC to the triangle DEF , fo is the prism having the triangle LXC for its base , and
OMN the triangle opposite to it , to the prism of which the base is the triangle RVF
, and the opposite triangle STY . and because the two prisms in the pyramid ...
Side 257
THEOR VERY prism having a triangular base may be divided into three pyramids
that have triangular bases , and are equal to one another . E Let there be a prism
of which the base is the triangle ABC , and let DEF be the triangle opposite to it ...
THEOR VERY prism having a triangular base may be divided into three pyramids
that have triangular bases , and are equal to one another . E Let there be a prism
of which the base is the triangle ABC , and let DEF be the triangle opposite to it ...
Side 262
Book XII . greater than the half of the circle ABCD + . upon the square ABCD bop
erect a prism of the fame altitude with the cylinder ; this prism is greater than half
of the cylinder ; because if a square be described about the circle , and a prism ...
Book XII . greater than the half of the circle ABCD + . upon the square ABCD bop
erect a prism of the fame altitude with the cylinder ; this prism is greater than half
of the cylinder ; because if a square be described about the circle , and a prism ...
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Vanlige uttrykk og setninger
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.
Bibliografisk informasjon
| Tittel | The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth The Elements of Euclid: Also the Book of Euclid's Data ...cor. Viz. The First Six Books, Together with the Eleventh and Twelfth, Robert Simson |
| Forfatter | Robert Simson |
| Utgiver | F. Wingrave, 1804 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Eksporter sitat | BiBTeX EndNote RefMan |