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

### From inside the book

Results 1-5 of 15

Page xiii

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**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 , 110 110 111 111 112 112 112 113 113 114 114 114 115 · 116 ... Page xiv

... square of the hypothenuse to the sum of the squares of the other two sides of a right triangle , 221. Comparative magnitude of an inscribed and circumscribed square , 222. To

... square of the hypothenuse to the sum of the squares of the other two sides of a right triangle , 221. Comparative magnitude of an inscribed and circumscribed square , 222. To

**construct a square**equivalent to two given squares , " 6 66 ... Page xv

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**construct**upon a given base a triangle similar to a given triangle , 141 • 142 142 144 274. 66 275. " 6 from the ...**square**, · . 149 · . 149 281. Ratio of the perimeters of similar triangles , 282. Ratio of the surfaces of similar ... Page 64

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**construct a square**upon a given straight line AB , ( fig . 69. ) Sol . 1. At the points A and B erect perpendicu- lars to the line AB . Take AC and BD each equal to AB . Draw CD and the required square will be constructed . Sol . 2. At ... Page 65

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**construct a square**which shall be double a given square , ( fig . 72. ) Sol . In the given square ABCD , draw the diagonal AC , and construct upon it the square AEFC , which square will be double the square ABCD . For ABCD is ...### 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.