## 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 34

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**side AC**of the acute angle BAC to depart more and more from AB , so as suc- cessively to reach AD , AE , and AF . By this move- ment , the mutual inclination of the sides AB and AC will be changed , and the angle BAC will become greater ... Page 52

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**side**of AB . Join C and D by a straight line . The line AB will be bisected at the point where CD crosses it . It is not necessary to describe entire circumferences ; 2 intersecting arcs on each**side**...**AC**, BC = BD , and AD = AE ... Page 53

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**side**of this point measure off in the line several small equal parts , for example 3 , viz . , AD , DH , HB ,**AC**, CG , GL . From A , as a centre , with a radius AB , describe a circumference . Then , on each**side**of the line AB ... Page 55

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**side AC**( fig . 39 ) departs from AB , the angle which it makes with AB is constantly in- creasing . Now let us suppose that each point in AC describes at the same time an arc of a circle . It is evident that such arcs bear a certain ... Page 56

... sides , may be taken as the measure of the angle , for they all contain the same number of degrees ; which number of degrees denotes the size of the angle . 60. If the

... sides , may be taken as the measure of the angle , for they all contain the same number of degrees ; which number of degrees denotes the size of the angle . 60. If the

**side AC**be moved entirely round the point A , it will have made 4 R ...### 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.