## Elements of Geometry |

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Page xi

If from the consequent of a ratio we subtract the antecedent , and compare the

If from the consequent of a ratio we subtract the antecedent , and compare the

**difference**with the antecedent , this last will be contained once less than it was in the first consequent ; the new ratio will be equal to the primitive ... Page xii

... In any proportion whatever , the sum of the two first terms is to the sum of the two last , and the

... In any proportion whatever , the sum of the two first terms is to the sum of the two last , and the

**difference**of the two first terms is to the**difference**of the two last , as the first is to the third , or as the second is ... Page xiii

... and the

... and the

**difference**of the antecedents is to the**difference**of the consequents , as one antecedent is to its consequent ; Whence it follows , that the sum of the antecedents is to their**difference**as the sum of the consequents is to ... Page 2

20 ) is the sum of the two angles DCB , BCE , and the angle DCB is the

20 ) is the sum of the two angles DCB , BCE , and the angle DCB is the

**difference**between the two angles DCE , BCE . Fig . 3 . 10. When a straight line AB ( fig . 3 ) meets another straight line CD in such a manner that the adjacent ... Page 31

If the distance CD of the centres of two circles is equal to the

If the distance CD of the centres of two circles is equal to the

**difference**of their radii CA , AD ( fig . 60 ) , these two circles will Fig . 60 . touch each other internally . Demonstration . In the first place , it is evident ...### What people are saying - Write a review

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### Common terms and phrases

ABC fig ABCD adjacent altitude applied base called centre chord circ circle circumference circumscribed common cone consequently construction contained convex surface Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces feet figure follows formed four give given greater half hence inclination inscribed intersection isosceles join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM produced proportional proposition pyramid radii radius ratio reason rectangle regular polygon respect right angles Scholium sector segment similar solid angle Solution sphere spherical square straight line suppose surface taken tangent THEOREM third triangle ABC vertex vertices whence