## 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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Praelect . ) “ That excepting a very few Interpolations , Explicati“ ons and Additions , Theon altered nothing in Euclid . ” But , by often considering and comparing together the Definitions and Demonstrations as they are in the

Praelect . ) “ That excepting a very few Interpolations , Explicati“ ons and Additions , Theon altered nothing in Euclid . ” But , by often considering and comparing together the Definitions and Demonstrations as they are in the

**Greek**... Page 74

And this is all that is to be understood , when in • the

And this is all that is to be understood , when in • the

**Greek**text and translations from it , the angle of the semicircle . ' is said to be greater than any acute rectilineal angle , and the re' maining angle less than any rectilineal ... Page 287

CRITICAL AND GEOMETRICAL ; CON T AINING , An Account of those Things in which this Edition differs from the

CRITICAL AND GEOMETRICAL ; CON T AINING , An Account of those Things in which this Edition differs from the

**Greek**Text ; and the Reafins of the Alterations which have been made . As also Observations on some of the Propositions . Page 290

B. I. Instead of this Definition as it is in the

B. I. Instead of this Definition as it is in the

**Greek**copies , a more distinct one is given from a property of a plane superficies , which is manifestly supposed in the Elements , viz . that a straight line draws from any point in a ... Page 292

... and its opposite fides are equal by 34. Prop . B. 1 . PROP . VII . B. I. There are two cases of this Proposition , one of which is not in the

... and its opposite fides are equal by 34. Prop . B. 1 . PROP . VII . B. I. There are two cases of this Proposition , one of which is not in the

**Greek**text , but is as necessary as the other . and that the case left out ...### 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.