## 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 20

Book 1. than the angle ACB ; but it is not ; therefore the

AB , and it has been shewn that it is not ... Let ABC be a triangle ; any two

it together are greater than the third

...

Book 1. than the angle ACB ; but it is not ; therefore the

**side**AC is not less thanAB , and it has been shewn that it is not ... Let ABC be a triangle ; any two

**sides**ofit together are greater than the third

**side**, viz . the**sides**BA , AC greater than the...

Page 23

Of the two

and at the point D in the straight line DE make * a . 23. 1 . the angle EDG equal to

the angle BAC ; and make DG equal bb . 3. 1 . to AC or DF , and join EG , GF .

Of the two

**sides**DE , DF let DE be the**side**which is not greater than the other ,and at the point D in the straight line DE make * a . 23. 1 . the angle EDG equal to

the angle BAC ; and make DG equal bb . 3. 1 . to AC or DF , and join EG , GF .

Page 24

ABC to DEF , and BCA to EFD ; also one

those

triangles , viz . BC to EF . the other

DE ...

ABC to DEF , and BCA to EFD ; also one

**side**equal to one**side**; and first , letthose

**sides**be equal which are adjacent to the angles that are equal in the twotriangles , viz . BC to EF . the other

**sides**shall be equal , each to each , viz . AB toDE ...

Page 395

V ratio which the two

triangle . therefore because two

the ratio of H to K must be the ratio of a greater to a less . bisect * the angle ...

V ratio which the two

**sides**about the angle EFG must have to the third**side**of thetriangle . therefore because two

**sides**of a triangle are greater than the third**side**,the ratio of H to K must be the ratio of a greater to a less . bisect * the angle ...

Page 440

The

given angle of the parallelogram , and ... FK be the given rectangle D to which the

sum of the squares of the

The

**sides**AB , BC and the parallelogram AC may be found thus . let EFG be thegiven angle of the parallelogram , and ... FK be the given rectangle D to which the

sum of the squares of the

**sides**is to be equal . and , by the preceeding case ...### 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.