## The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth |

### Inni boken

Resultat 1-5 av 5

Side 218

Book XI . multiple foever the base LF is of the bafe AF , the same multiple is w the

the base HF , the same multiple is the

Book XI . multiple foever the base LF is of the bafe AF , the same multiple is w the

**folid**LV of the solid AV . for the same reason , whatever multiple the base NF is ofthe base HF , the same multiple is the

**folid**NV of the**folid**ED . and if the base ... Side 225

AE to the solid LR . for the same reason , because the

cut by the plane LMFD which is parallel to the opposite planes CP , BR ; as the

base CD P K R. to the base LQ , so N is the solid CF to the V X G )

as ...

AE to the solid LR . for the same reason , because the

**folid**parallelepiped CR iscut by the plane LMFD which is parallel to the opposite planes CP , BR ; as the

base CD P K R. to the base LQ , so N is the solid CF to the V X G )

**folid**LR . butas ...

Side 227

have their insisting straight lines at right angles to the bases . and Book XI . the

solid EQ_is equal to the solid AE ; and the

because they are upon the fame bafes and of the fame altitude . therefore the

solid ...

have their insisting straight lines at right angles to the bases . and Book XI . the

solid EQ_is equal to the solid AE ; and the

**folid**FY to 1. 29. or 30 . the**folid**CF ;because they are upon the fame bafes and of the fame altitude . therefore the

solid ...

Side 230

C. II .

of which is AS , and of which AO is one of its infifting straight lines . Take any

straight line a , and as MA to AP , so make a to b ; and as NA to AQ , so make b to

c ...

C. II .

**folid**AX is equal a to the**folid**CD . complete likewise the**folid**AY the baseof which is AS , and of which AO is one of its infifting straight lines . Take any

straight line a , and as MA to AP , so make a to b ; and as NA to AQ , so make b to

c ...

Side 234

234 Book XI . altitude of the

bases of the solid parallelepipeds AB , CD are reciprocally proportional to their

altitudes . Next , Let the bases of the solids AB , CD be reciprocally proportional

to ...

234 Book XI . altitude of the

**folid**CD to the altitude of the solid AB ; that is , thebases of the solid parallelepipeds AB , CD are reciprocally proportional to their

altitudes . Next , Let the bases of the solids AB , CD be reciprocally proportional

to ...

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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.