## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., Enl |

### From inside the book

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**Magnitudes**may be considered under three dimensions , -length , breadth , height or thickness .. 2. In Geometry there are several general terms or principles ; such as , Definitions , Propositions , Axioms , Theorems , Problems , Lemmas ... Page 8

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**magnitude**. " ( See Notes . ) 2. A line is length without breadth . " COROLLARY . The extremities of a line are points ; and the intersections " of one line with another are also points . " 3. " If two lines are such that they cannot ... Page 11

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**Magnitudes**which coincide with one another , that is , which exactly fill the same space , are equal to one another . 9. The whole is greater than its part . 10. All right angles are equal to one another . வ 11. " Two straight lines ... Page 106

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**magnitude**of any kind , it signifies that the "**magnitude**is multiplied by the number . Thus , 3A signifies three " times A ; mB , m times B , or a multiple of B by m . When the num " ber is intended to multiply two or more**magnitudes**... Page 107

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**Magnitudes**are said to be of the same kind , when the less can be mul- tiplied so as to exceed the greater ; and it is only such**magnitudes**that are said to have a ratio to one another . 5. If there be four**magnitudes**, and if any ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore