## The Elements of Euclid; viz. the first six books,together with the eleventh and twelfth, with an appendix |

### From inside the book

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Page 10

... triangle ABC to the

... triangle ABC to the

**triangle DEF**; and the other angles to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . For , if the triangle ABC be applied ... Page 11

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**DEF**, and the angle ACB to DFE . Therefore , if two**triangles**have two sides of the one equal to two sides of the ...**triangle**are equal to one another ; and if the equal sides be produced , the angles upon the other side of the ... Page 14

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**triangle**ACD , AC is equal to AD , the angles ECD , FDC upon the other side of the base CD are equal to one another ...**DEF**be two**triangles**, having the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to ... Page 15

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**triangle DEF**; then join AF : the straight line AF shall bisect the angle BAC . D F C Because AD is equal to AE , and AF is common to the two triangles B DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to ... Page 25

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**triangle**KFG shall have its sides equal to the three straight lines , A , B , C. Because the point F is the centre of the circle DKL , FD is equal to FK ; but FD is equal to the straight * 15**Def**. line A ; therefore FK is equal to A ...### Other editions - View all

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |

### Common terms and phrases

AB is equal AC is equal altitude angle ABC angle ACB angle BAC base BC bisect centre circle ABCD circle EFGH circumference common section cone cylinder demonstrated described diameter draw equal to F equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prisms PROB proved pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD sphere square of AC straight line AC THEOR third three plane angles three straight lines tiples touches the circle triangle ABC triangle DEF triplicate ratio twice the rectangle wherefore whole

### Popular passages

Page 173 - 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 56 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 53 - 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 on the line between the points of section, is equal to the square on half the line.

Page 58 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

Page 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Page 23 - Any two sides of a triangle are together greater than the third side.

Page 40 - EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels.

Page 103 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square on the line which touches it.

Page 50 - PROP. I. THEOR. If there oe two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 28 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.