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

### From inside the book

Results 6-10 of 17

Page 141

... sides are opposite to the equal angles . 269. From the preceding propositions we learn that the similarity of two ...

... sides are opposite to the equal angles . 269. From the preceding propositions we learn that the similarity of two ...

**homologous sides**of the other , and the included angles equal . 3. If the three sides of the one are proportional ... Page 144

... sides and an- gles of the field . Suppose the side AB is 100 rods long ; draw the line a b one inch long , and it ...

... sides and an- gles of the field . Suppose the side AB is 100 rods long ; draw the line a b one inch long , and it ...

**homologous angles**of the other ; and the sides of the one are proportional to the**homologous sides**of the other ... Page 148

... angles are proportional . In the triangles ABD and ABC , angle BAD ACB ; thus BD and BA are homo- logous sides , and since angle BDA BAC , therefore - = BA and BC are

... angles are proportional . In the triangles ABD and ABC , angle BAD ACB ; thus BD and BA are homo- logous sides , and since angle BDA BAC , therefore - = BA and BC are

**homologous sides**. Hence we have 148 COMPARISON AND MENSURATION . Page 149

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**homologous sides**. Hence we have this proportion , BD : BA : = BA : BC . From the similarity of the triangles ADC and ABC we have the proportion , CD : CA = CA : CB . 3. The perpendicular AD is a mean proportional between the two parts ... Page 150

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**homologous sides**. 282. What is the ratio of the surface of the triangle ABC to that of the similar triangle DEF ? Sol . Suppose triangle ABC to be placed upon DEF , so that its sides shall exactly coincide with those of the triangle ...### 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.