## 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

Side 17

And in like manner , it may be demonstrated that no other can be in the same

straight line with it but BD , which therefore is in the same straight line with CB .

Wherefore if at a point , & c . Q. E. D. ..PROP . XV .

lines cut ...

And in like manner , it may be demonstrated that no other can be in the same

straight line with it but BD , which therefore is in the same straight line with CB .

Wherefore if at a point , & c . Q. E. D. ..PROP . XV .

**THEOR**. $ Il F two straightlines cut ...

Side 115

I.

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 of magnitudes AB , CD

...

I.

**THEOR**. I F any number of magnitudes be equimultiples of as many , each ofeach ; 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 of magnitudes AB , CD

...

Side 122

Also the Book of Euclid's Data ...cor. viz. The first six books, together with the

eleventh and twelfth Robert Simson. Book V. any whatever of A and C. Therefore

as B is to A , fo is D to C. If then four magnitudes , & c . Q. E. D. PROP . C.

.

Also the Book of Euclid's Data ...cor. viz. The first six books, together with the

eleventh and twelfth Robert Simson. Book V. any whatever of A and C. Therefore

as B is to A , fo is D to C. If then four magnitudes , & c . Q. E. D. PROP . C.

**THEOR**.

Side 191

part above it . If it be possible , " let AB part of the straight line ABC be in the plane

, and the part BC above it and since the straight line AB is in the plane , it can be

...

**THEOR**. ON NE part of a straight line cannot be in a plane and See N. anotherpart above it . If it be possible , " let AB part of the straight line ABC be in the plane

, and the part BC above it and since the straight line AB is in the plane , it can be

...

Side 214

Q. E. D. PROP . B.

three plane angles which are equal to one another , each to each , and alike

situated ; these solid angles are equal to one another . Let there be two folid

angles at A ...

Q. E. D. PROP . B.

**THEOR**. See N. F two solid angles be contained , each bythree plane angles which are equal to one another , each to each , and alike

situated ; these solid angles are equal to one another . Let there be two folid

angles at A ...

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### 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.