## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |

### From inside the book

Results 1-5 of 5

Page 18

THEOR F one Gide of a triangle be produced , the exterior angle is greater than

either of the interior

be produced to D. the exterior angle ACD is greater than either of the interior ...

THEOR F one Gide of a triangle be produced , the exterior angle is greater than

either of the interior

**opposite**angles . Let ABC be a triangle , and let its side BCbe produced to D. the exterior angle ACD is greater than either of the interior ...

Page 31

each to each , to which the equal fides are

ACB is equal to the angle CBD , and becaufe the straight linem BC meets the two

straight lines AC , BD and makes the alternate angles ACB , CBD equal to one ...

each to each , to which the equal fides are

**opposite**. therefore the Book I. angleACB is equal to the angle CBD , and becaufe the straight linem BC meets the two

straight lines AC , BD and makes the alternate angles ACB , CBD equal to one ...

Page 222

11.

AGHC . therefore the D K folid AH is double of the prism which is contained by

the triN angles ALG , CBH . for the fame reason , because the folid C B AK is cut

by ...

11.

**opposite**planes ALGF , CBHD , AH is cut into two equal parts by the planeAGHC . therefore the D K folid AH is double of the prism which is contained by

the triN angles ALG , CBH . for the fame reason , because the folid C B AK is cut

by ...

Page 251

angle that is half of the parallelogram , these prisms are equal to Book XII . one

another ; therefore the prism having the parallelogram EBFG for its base , and the

straight line KH

angle that is half of the parallelogram , these prisms are equal to Book XII . one

another ; therefore the prism having the parallelogram EBFG for its base , and the

straight line KH

**opposite**to it , is equal to the 1.40.11 . prism having the triangle ... Page 253

RVF , and the

ABCG are equal to one another , and also the two prisms in the pyramid DEFH

equal to one another , as the prism of which the base is the parallelogram KBXL ...

RVF , and the

**opposite**triangle STY . and because the two prisms in the pyramidABCG are equal to one another , and also the two prisms in the pyramid DEFH

equal to one another , as the prism of which the base is the parallelogram KBXL ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

added alſo altitude angle ABC angle BAC baſe BC is given 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 reaſon rectangle remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole

### Popular passages

Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 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.

Page 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.

Page 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...

Page 105 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Page 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Page 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

Page 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Page 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Page 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.