## An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books |

### From inside the book

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Page xii

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**parallelograms**, 152. A triangle equivalent to half a**parallelogram**of equal base and altitude , 153. Case of equivalent triangles , 154. Sum of the angles of a polygon , 155. Value of each angle of a regular polygon , 156. Value of ... Page xiii

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**parallelogram**into an equivalent triangle , 213. To construct a square 1 times as great as a given square , 214. To transform a triangle into an equivalent**parallelogram**, 215. Two diagonals in a**parallelogram**bisect each other , 110 ... Page xiv

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**parallelograms**into unequal parts , 218. To divide a**parallelogram**into 2 , 3 , 4 , or more equal parts , 119 219. A straight line drawn through the middle of a diagonal of a**parallelogram**bisects the**parallelogram**, • · • 220. Ratio of ... Page xv

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**parallelograms**of equal bases , triangles of unequal bases and unequal altitudes ,**parallelograms**in general to one another , the parts into which the sides of a triangle are divi- ded by a line parallel to the base , such parallel line ... Page 7

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**parallelogram**. 5. 2**parallelograms**; one with right angles , and the other with oblique angles . 6.**Parallelograms**in which two of the sides shall be twice , thrice , 4 times longer than the other two . 7. A**parallelogram**having its ...### Other editions - View all

### Common terms and phrases

adjacent angles angle BAC angles are equal Bisect centre chord circumference coincide concave angles consequently angle construct a square convex angle convex surface cube curved line cylinder decagonal describe a circle diagonals diameter divided division points draw a line Draw a straight equal altitude equal angles equal bases equivalent erect a perpendicular exterior angles feet found by multiplying given number given square greatest number hexagon homologous sides hypothenuse inches inscribed circle isosceles triangle length let fall line drawn line passes magnitude measured Multiply the number number of lines number of points number of straight opposite parallelogram parallelopiped passes 2 points pendicular pentagon proportion protractor quadrilateral radii radius equal ratio regular polygon right angle semi-circumference set intersecting side AC similar similar triangles solidity sphere straight line suppose tangents triangle ABC triangular prism unequal vertex vertices

### Popular passages

Page 130 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.

Page 154 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.