## 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. Martin1874 |

### From inside the book

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**have an angle of the one equal to an angle of the other , and**if , also , the sides of the two figures , about each of their angles , be proportionals , the remaining angles of the one shall be equal to the remaining angles of the other ...### Other editions - View all

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

### Common terms and phrases

AC is equal adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angle equal base BC bisected centre circle ABC circumference constr Demonstration diameter double equal angles equal to F equiangular equilateral triangle equimultiples ex æquali exterior angle fourth given circle given point given straight line gnomon greater ratio inscribed less Let ABC Let the straight linear units meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon produced proportionals Q.E.D. PROPOSITION quadrilateral rectangle contained remaining angle right angles segment semicircle similar square on AC straight line AB straight line BC straight line drawn three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore

### Popular passages

Page 1 - 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 6 - 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 232 - 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 112 - 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 209 - ... 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 269 - 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 199 - 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 23 - 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 63 - 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 32 - ... 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.