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

### From inside the book

Page 10

...

...

**line**. If the chord**passes**through the centre of the circle it is called a diameter , and it will divide the circle and its circumference into two equal parts , called respectively semi - circles and semi - circum- ferences . A straight ... Page 31

... 3 R. 2 R. 1 ac . 2 R. 1 ob . 1 R. 1 ac . 1 ob . 2 ob . 1 ac . 1 ob . 2 ac . 3. When 1

... 3 R. 2 R. 1 ac . 2 R. 1 ob . 1 R. 1 ac . 1 ob . 2 ob . 1 ac . 1 ob . 2 ac . 3. When 1

**line passes**2 points , ( fig . 26. ) 4 R. 2 R. 1 ob . 1 ac . 2 ob . 2 ac . 4. When 2**lines pass**beyond the junction - points 5 ANGLES . 31. Page 32

... lines meeting at 3 points . 1. When no

... lines meeting at 3 points . 1. When no

**line passes**a junction - point , ( fig . 29. ) 1 R. 2 ac . 1 ob . 2 ac . 3 ac . 2. When 1**line passes**1 point , ( fig . 30. ) 2 R. 2 ac . 1 R. 1 ob . 2 ac . 2 ac . 2 ob . 1 ob . 3 ac . 3. When 1 line ... Page 33

...

...

**lines pass**1 point each , ( fig . 35. ) 2 R. 2 ob . 2 ac . 1 R. 3 ob . 3 ac . 3 ob . 3 ac . 4 ob . 3 ac . 4 R. 1 ob . 2 ac . 3 ob . 4 ac . 2 R. 2 ob . 3 ac . 8. When 1**line passes**2 points , and 2**lines pass**1 point each , ( fig . 36 ... Page 50

...

...

**line**of any length ; open the com-**passes**so that the points shall be 1 inch apart , or , as it is more concisely expressed , take 1 inch between the points of the compasses , and apply them to the**line**. To get the 2d**line**, apply ...### 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.