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 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 ...
Side 272
... and are therefore all equal to one anoB.15 Def.1 . ther . therefore the line GH is
the circumference of a circle 6 of which the center is the point K. therefore the
plane GH divides the cylinder AD into the cylinders AH , GD ; for they are the
same ...
... and are therefore all equal to one anoB.15 Def.1 . ther . therefore the line GH is
the circumference of a circle 6 of which the center is the point K. therefore the
plane GH divides the cylinder AD into the cylinders AH , GD ; for they are the
same ...
Side 273
KF and cylinder GD , any equimultiples whatever , viz . the axis Book XII . KM and
cylinder GQ , and it has been demonstrated if the axis KL be greater than the axis
KM , the cylinder PG is greater than the cylinder GQ ; and if equal , equal , and ...
KF and cylinder GD , any equimultiples whatever , viz . the axis Book XII . KM and
cylinder GQ , and it has been demonstrated if the axis KL be greater than the axis
KM , the cylinder PG is greater than the cylinder GQ ; and if equal , equal , and ...
Side 274
See N. THE " HE bases and altitudes of equal cones and cylinders are
reciprocally proportional ; and if the bases and altitudes be reciprocally
proportional , the cones and cylinders are equal to one another . b , A. 5 . 3 Let
the circles ABCD ...
See N. THE " HE bases and altitudes of equal cones and cylinders are
reciprocally proportional ; and if the bases and altitudes be reciprocally
proportional , the cones and cylinders are equal to one another . b , A. 5 . 3 Let
the circles ABCD ...
Side 275
But let the bases and altitudes of the cylinders AX , EO , be reciprocally
proportional , viz . the base ABCD to the base EFGH , as the altitude MN to the
altitude KL . the cylinder AX is equal to the cylinder EO . First , let the base ABCD
be equal ...
But let the bases and altitudes of the cylinders AX , EO , be reciprocally
proportional , viz . the base ABCD to the base EFGH , as the altitude MN to the
altitude KL . the cylinder AX is equal to the cylinder EO . First , let the base ABCD
be equal ...
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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 |