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

### From inside the book

Results 1-5 of 24

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**polygons**, by more than four straight lines . XXIV . Of three - sided figures , an equilateral tri- angle is that which has three equal sides . XXV . An isosceles triangle is that which has only two sides equal . XXVI . A scalene ... Page 125

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**polygons**treated of in this Book , and those which may be derived from them by successive bisections of the ...**polygon**of 17 sides may be inscribed in a circle , for 17 is a prime number , that is , a number which is not ... Page 191

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**polygons**may be divided into the same number of similar triangles , having the same ratio to one another that the**polygons**have ; and the**polygons**have to one another the duplicate ratio of that which their homologous sides have . Let ... Page 192

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**polygons**have ; and the**polygon**ABCDE shall have to the**polygon**FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the**polygon**ABCDE is similar to the**polygon**FGHKL , the angle ... Page 193

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**polygon**FGHKL the duplicate ratio of that which the side AB has to the homologous side FG . Because the triangle ABE ...**polygon**ABCDE to the**polygon**FGHKL : but the triangle ABE has to the triangle FGL , the duplicate ratio * of ...### 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.