## 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 |

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1 ence by which the Investigation and Discovery of useful Truths , at least in Mathematical Learning , is promoted as far as the limited Powers of the Mind allow ; and which

1 ence by which the Investigation and Discovery of useful Truths , at least in Mathematical Learning , is promoted as far as the limited Powers of the Mind allow ; and which

**likewise**is of the greatest Use in the Arts both of Peace and ... Page 8

Post . ftance AD describe b the circle DEF . and because A is the center of the circle DEF , AE shall be equal to AD , but the straight line C is

Post . ftance AD describe b the circle DEF . and because A is the center of the circle DEF , AE shall be equal to AD , but the straight line C is

**likewise**equal to ' AD . whence AE and C are each of them equal to c . 1. Page 9

Therefore if two triangles have two sides of the one equal to two sides of the other , each to each , and have

Therefore if two triangles have two sides of the one equal to two sides of the other , each to each , and have

**likewise**the angles contained by those sides equal to one another ; their bases shall**likewise**be equal , and the triangles ... Page 11

ON the same base , and on the same side of it , See N. there cannot be two triangles that have their sides which are terminated in one extremity of the base equai to one another , and

ON the same base , and on the same side of it , See N. there cannot be two triangles that have their sides which are terminated in one extremity of the base equai to one another , and

**likewise**those which are terminated in the other ... Page 12

... the angles ECD , FDC upon the other side of the base CD are equal one another ; but the angle ECD is greater than the angle BCD , wherefore the angle FDC is

... the angles ECD , FDC upon the other side of the base CD are equal one another ; but the angle ECD is greater than the angle BCD , wherefore the angle FDC is

**likewise**greater than BCD ; much more then is the angle BDC greater than ...### What people are saying - Write a review

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### Common terms and phrases

added alſo altitude angle ABC angle BAC baſe BC is given becauſe Book caſe circle circle ABCD circumference common cone contained 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 BC 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.