## 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 xi

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**line**, 99. What is meant by measuring . Units of measure , 100. In what ...**lines**by a third**line**, 106 . to 111 . · Of the magnitude of the angles thus ...**drawn**obliquely to a perpendicular , 138. Case of equal triangles , 139 ... Page xiv

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**line drawn**through the middle of a diagonal of a parallelogram bisects the parallelogram , • · • 220. Ratio of the square of the hypothenuse to the sum of the squares of the other two sides of a right triangle , 221. Comparative ... Page 4

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**Draw**, in each of the foregoing 8 directions , 6 ...**line**. 2. Angles .**Draw**two straight**lines**which shall be perpendicular to one another , and thus make a right angle . Make right angles in all the positions in which you have**drawn**... Page 9

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**lines**may be**drawn**in it . We can suppose a straight**line**joining the middle of the bases ; this is the axis of the cylinder . If we suppose a rectangle to revolve about one of its sides as an axis , the side opposite to this axis will ... Page 10

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**drawn**from the centre to any point in the circumference is called a radius . Two radii**drawn**in directly opposite directions form a diameter . A straight**line**which , however far it may be produced in both directions , touches the ...### 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.