## 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 9

D gle BAC equal to the angle EDF . the base BC

and the triangle ABC to the triangle DEF ; and the other angles , to which the

equal sides are opposite , thall be equal , each B CE to each , viz . the angle ABC

to ...

D gle BAC equal to the angle EDF . the base BC

**shall**be equal to the base EF ;and the triangle ABC to the triangle DEF ; and the other angles , to which the

equal sides are opposite , thall be equal , each B CE to each , viz . the angle ABC

to ...

Side 115

PROP . I. THEOR . I F any number of magnitudes be equimultiples of as many ,

each of each ; what multiple soever any one of them is of its part , the same

multiple

magnitudes ...

PROP . I. THEOR . I F any number of magnitudes be equimultiples of as many ,

each of each ; what multiple soever any one of them is of its part , the same

multiple

**shall**all the first magnitudes be of all the othet . Let any number ofmagnitudes ...

Side 138

Let A , B , C be three magnitudes , and D , E , F other three which have the same

ratio taken two and two , but in a cross order , viz . as A is to B , so is E to F , and

as B is to C , so is D to E. If A be greater than C , D

...

Let A , B , C be three magnitudes , and D , E , F other three which have the same

ratio taken two and two , but in a cross order , viz . as A is to B , so is E to F , and

as B is to C , so is D to E. If A be greater than C , D

**shall**be greater than F ; and if...

Side 371

The first six books, together with the eleventh and twelfth Robert Simson. b . 12. 5

. and if this ratio be the same with A B TC the ratio of AB to CD , the ratio of AE to

CF , which is the fame with C D F the given ratio of AB to CD ,

The first six books, together with the eleventh and twelfth Robert Simson. b . 12. 5

. and if this ratio be the same with A B TC the ratio of AB to CD , the ratio of AE to

CF , which is the fame with C D F the given ratio of AB to CD ,

**shall**be given . Side 376

Also if the first has a given ratio to the second , and the excess of the third above

a given magnitude has also a given ratio to the second , the same excess

have a given ratio to the first ; as is evident from the oth Dat . 17 . PROP . XXV .

Also if the first has a given ratio to the second , and the excess of the third above

a given magnitude has also a given ratio to the second , the same excess

**shall**have a given ratio to the first ; as is evident from the oth Dat . 17 . PROP . XXV .

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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.