## Euclidian Geometry |

### From inside the book

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**Chords**. Sup . to Book I. I 2 18 2. I , 3 a 19 b 20 C 21 3454 ......... 9 14 15 A 18 25 24 .25 22 .23 6 Tangents . 16 , 18 , 19 F k B 17 เ с m ........ R II . 9 , 10 Parallels . Lemma . n Contact of S. .31 p 2 20 ......... 27 , 28 Չ 7 ... Page 94

... ( HG , HS ) , and .. four times rectangle ( AB , BC ) . = .. square on AC is greater than square on AD by four times rectangle ( AB , BC ) .

... ( HG , HS ) , and .. four times rectangle ( AB , BC ) . = .. square on AC is greater than square on AD by four times rectangle ( AB , BC ) .

**CHORDS**. DEFINITION . The straight line joining any two 94 SUPPLEMENT TO BOOK II . Page 95

Francis Cuthbertson.

Francis Cuthbertson.

**CHORDS**. DEFINITION . The straight line joining any two points in the circum- ference of a circle is called a**chord**of the circle . PROPOSITION I. The straight line joining any two points in the circum- ference of a ... Page 96

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**chord**. H B Let AB be a**chord**of a of which C is the centre . Then the straight line CH through C and the middle point H of AB shall be to AB . Join CA , CB . Then . AH , HC , CA are respectively BH , HC , CB ; .. ' . LAHC = = L BHC ... Page 97

... SH is to PQ . ( 1.5 ) .. the centre of the C is in the straight line HS . ( 111.2 ) Similarly it is in the straight line KS ; .. S is the centre of the © PQR . C. G. 7 DEFINITION . Straight lines are said to be equally distant

... SH is to PQ . ( 1.5 ) .. the centre of the C is in the straight line HS . ( 111.2 ) Similarly it is in the straight line KS ; .. S is the centre of the © PQR . C. G. 7 DEFINITION . Straight lines are said to be equally distant

**CHORDS**. 97.### Other editions - View all

### Common terms and phrases

base bisect Cambridge centre chapter chord circle circumference classes cloth College common complete construction contained Crown 8vo DEFINITION describe diameter difference divided double draw drawn Edition elementary English equal equiangular Examination Examples extremities fall fcap figure former four GEOMETRY given point given straight line Grammar greater Hence Illustrations impossible inscribed introduction Join language Latin less magnitudes Master Mathematical meet method Notes opposite parallel parallelogram pass perimeter perpendicular plane polygon possible present principles PROBLEM produced Professor proportional PROPOSITION prove ratio reading rect rectangle render respectively revised right angles Schools Second Edition segment selected sides similar Similarly square student taken tangent THEOREM third touch TREATISE triangle twice University volume whole

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Page 157 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

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