## The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected; and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. the first six books, together with the eleventh and twelfth |

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Page 11

... three sided figures , an equilateral triangle is that which has three equal

XXV . , An isosceles triangle , is that which has only two

1 . ΔΔΔ XXVI . A scalene triangle , OF EUCLID : XV. ...

... three sided figures , an equilateral triangle is that which has three equal

**fides**.XXV . , An isosceles triangle , is that which has only two

**fides**equal . XXVI , Book1 . ΔΔΔ XXVI . A scalene triangle , OF EUCLID : XV. ...

Page 12

A scalene triangle , is that which has three unequal

triangle , is that which has a right angle . XXVIII . An obtuse angled triangle , is

that which has an obtuse angle . 44 XXIX . An acute angled triangle , is that which

...

A scalene triangle , is that which has three unequal

**fides**. XXVII . A right angledtriangle , is that which has a right angle . XXVIII . An obtuse angled triangle , is

that which has an obtuse angle . 44 XXIX . An acute angled triangle , is that which

...

Page 16

... each to each ; and have likewise the angles contained by those

one another ; they shall likewise have their bales , or third

two triangles fhail be equal ; and their other angles shall be equal , cach to each

...

... each to each ; and have likewise the angles contained by those

**fides**equal toone another ; they shall likewise have their bales , or third

**fides**, equal ; and thetwo triangles fhail be equal ; and their other angles shall be equal , cach to each

...

Page 17

A D to the angle EDF , the base BC shall be equal to the base EF ; and the

triangle ABC to the triangle DEF ; and the other angles , to which the equal

are opposite , shall be equal each to each , viz . the angle ABC to the angle DEF ,

and ...

A D to the angle EDF , the base BC shall be equal to the base EF ; and the

triangle ABC to the triangle DEF ; and the other angles , to which the equal

**fides**are opposite , shall be equal each to each , viz . the angle ABC to the angle DEF ,

and ...

Page 18

Ax . mainder BF shall be equal to the remainder CG ; and FC was proved to be

equal to GB ; therefore the two

to each ; and the angle BFC is equal to the angle CGB , and the bafe BC is ...

Ax . mainder BF shall be equal to the remainder CG ; and FC was proved to be

equal to GB ; therefore the two

**fides**BF , FC are equal to the two CG , GB , eachto each ; and the angle BFC is equal to the angle CGB , and the bafe BC is ...

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### Common terms and phrases

added alſo altitude angle ABC angle BAC baſe 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 magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane produced prop proportionals propoſition pyramid radius rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC Take taken theſe third triangle ABC wherefore whole

### Popular passages

Page 32 - 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 165 - 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.

Page 170 - 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 10 - When several angles are at one point B, any ' one of them is expressed by three letters, of which ' the letter that is at the vertex of the angle, that is, at ' the point in which the straight lines that contain the ' angle meet one another, is put between the other two ' letters, and one of these two is...

Page 55 - 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 32 - ... then shall the other sides 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, BCA equal to the angles DEF, EFD, viz.

Page 45 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Page 211 - AB shall be at right angles to the plane CK. Let any plane DE pass through AB, and let CE be the common section of the planes DE, CK ; take any point F in CE, from which draw FG in the plane DE at right D angles to CE ; and because AB is , perpendicular to the plane CK, therefore it is also perpendicular to every straight line in that plane meeting it (3.

Page 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 304 - Thus, if B be the extremity of the line AB, or the common extremity of the two lines AB, KB, this extremity is called a point, and has no length : For if it have any, this length must either be part of the length of the line AB, or of the line KB.