## The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin |

### From inside the book

Page 12

For , if the triangle

For , if the triangle

**ABC**be applied to the triangle DEF , so that the point A**may**be on D , and the straight line AŘ on DE ... The angles at the**base**of an**isosceles triangle**are**equal**to each**other**; and if the**equal sides**be produced ... Page 13

**Let ABC**be an**isosceles triangle**of which the**side AB**is**equal**to AC , and**let**the**equal sides AB**, AC be produced to D and E. Then the angle**ABC shall**be**equal**to the angle ACB , and the angle DBC to the angle ECB . Page 148

**Let**ABCD be the given square . ... Because DA is**equal**to**AB**, and AC common to the**triangles**DAC , BAC ( I. Def . 30 ) , the two**sides**DA , AC are**equal**to the two BA , AC , each to each ; and the**base**DC is**equal**to the**base**BC ...### What people are saying - Write a review

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The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides No preview available - 2016 |

### Common terms and phrases

ABCD AC is equal alternate angle ABC angle ACB angle BAC base base BC bisected centre circle ABC circumference common compounded constr Construction contained Demonstration describe diameter divided double draw equal angles equiangular equimultiples exterior angle extremities fall figure four fourth given point given straight line greater half inscribed interior join less Let ABC likewise magnitudes manner meet multiple opposite angle parallel parallelogram pass perpendicular plane polygon Problem produced proportionals proved Q.E.D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar square square on AC taken third touches the circle triangle ABC unequal wherefore whole

### Popular passages

Page 4 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Page 230 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...

Page 110 - 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 207 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.

Page 267 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 197 - 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 21 - 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.

Page 61 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...

Page 30 - ... twice as many right angles as the figure has sides ; 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.