## 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 7

Side 36

Book I. Let the parallelogram ABCD and the triangle EBC be upon Mthe

base BC , and between the

double of the A DE Join AC ; then the triangle ABC a . 37. I. equal a to the triangle

...

Book I. Let the parallelogram ABCD and the triangle EBC be upon Mthe

**fame**base BC , and between the

**fame**parallels BC , AE ; the parallelogram ABCD isdouble of the A DE Join AC ; then the triangle ABC a . 37. I. equal a to the triangle

...

Side 123

Ik F the first be to the second as the third to the fourth , See N. and if the first be a

multiple , or part of the second ; the third is the

the fourth . b . A. 5 . Let A be to B , as C is to D ; and first let A be a multiple of B ...

Ik F the first be to the second as the third to the fourth , See N. and if the first be a

multiple , or part of the second ; the third is the

**fame**multiple , or the**fame**part ofthe fourth . b . A. 5 . Let A be to B , as C is to D ; and first let A be a multiple of B ...

Side 141

Let AB the first here to C the second the

the fourth ; and let BG the fifth have to C the second the same ratio , which EH the

fixth has to F the fourth . AG , the first G and fifth together , shall have to C the seH

...

Let AB the first here to C the second the

**fame**ratio , which DE the third has to Fthe fourth ; and let BG the fifth have to C the second the same ratio , which EH the

fixth has to F the fourth . AG , the first G and fifth together , shall have to C the seH

...

Side 149

33. sa diculars are both equal and parallel to one another . then , if the

construction be made as in the Propofition , the Demonstration will be the same .

PROP . II . THEOR . I F a straight line be drawn parallel to one of the sides See N.

of ...

33. sa diculars are both equal and parallel to one another . then , if the

**fame**construction be made as in the Propofition , the Demonstration will be the same .

PROP . II . THEOR . I F a straight line be drawn parallel to one of the sides See N.

of ...

Side 262

Book XII . greater than the half of the circle ABCD + . upon the square ABCD bop

erect a prism of the

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 halfof 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.