## 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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**radii**drawn in directly opposite directions form a diameter . A straight line which , however far it may be produced in both directions , touches the circumference only at one point , is called a tangent : the point where it touches the ... Page 49

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**radii**, by so much of the straight line joining the 2 cen- tres as lies between the 2 circumferences . In 3 the distance between the 2 centres is equal to the sum of the 2**radii**. In 4 the distance is less than the sum of the 2**radii**by ... Page 50

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**radii**. 50. Suppose it is required to draw 10 straight lines , of which the 1st shall be 1 inch long , the 2d 2 inches long , and the 3d 3 inches long , and so on , the 10th being 10 inches long . Draw a straight line of any length ... Page 51

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**radii**of the same circle , ) then the first circle will meet the 2d at one point only , viz . at E. - 4. Having the surface of one in common , without the circumferences touching each other , ( fig . 46. 5. ) Pro- duce AB to C. From A ... Page 52

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**radii**, which must be greater than AB , describe two circles ; the circumferences of these circles will intersect at 2 points , C and D , one on each side of AB . Join C and D by a straight line . The line AB will be bisected at 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.