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

### From inside the book

Page 23

... 1. Between 2 points , only 1 straight line can be drawn , and these determine the length and position of the line ; a straight line , drawn from the 1st point to the 2d , will

... 1. Between 2 points , only 1 straight line can be drawn , and these determine the length and position of the line ; a straight line , drawn from the 1st point to the 2d , will

**coincide**with a straight line drawn from 4 * LINES . 23. Page 24

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**coincide**with a straight line drawn from the 2d to the 1st . To**coincide**is to fall on , and exactly fill the same space . 2. Between 3 points . In this case we may have 3 distinct straight lines , viz . , from the 1st point to the ... Page 34

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**coincides**with AG ; then BAG can be consid- ered as an angle ; this angle , which is greater than 2 R. A. , is called a convex angle . All angles not convex are concave angles . Obtuse , right , and acute angles are Wherever there is a ... Page 57

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**coincide**, the sides of the square do not form exactly a right angle . The angle COD will be twice the differ- ence between the angle made by the 2 sides and a right angle . 63. Having examined the construction of these in- struments ... Page 61

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**coincide**entirely when one is laid upon the other ; therefore equal figures must be similar . 71. To construct triangles in and about circles . 1. An equilateral triangle , ( fig . 63. ) Divide the cir- cumference of a circle with 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.