## Elements of Geometry and Trigonometry |

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Page 13

The

The

**whole**is greater than any of its parts . 9. The**whole**is equal to the sum of all its parts . 10. All right angles are equal to each other . 11. From one point to another only one straight line can be drawn . 12. Page 14

THEOREM .. straight lines , which have two points common , coincide with each other throughout their

THEOREM .. straight lines , which have two points common , coincide with each other throughout their

**whole**extent , and form one and the same straight line . Let A and B be the two common points . In the first place it is evident that ... Page 21

But the part cannot be equal to the

But the part cannot be equal to the

**whole**( Ax . 8. ) ; hence , there is no inequality between the sides BA , AC ; therefore , the triangle BAC is isosceles . PROPOSITION XIII . THEOREM . Page 22

and E B the line CD would coincide with CE ; otherwise , a part would be equal to the

and E B the line CD would coincide with CE ; otherwise , a part would be equal to the

**whole**, which is impossible ( Ax . 8. ) . PROPOSITIOŃ XV . THEOREM . If from a point without a straight line , a perpendicular be let fall on the line ... Page 34

Thus , of two magnitudes , one of them may be considered to be divided into some number of equal parts , each of the same kind as the

Thus , of two magnitudes , one of them may be considered to be divided into some number of equal parts , each of the same kind as the

**whole**, and one of those parts being considered as an unit of measure , the magnitude may be expressed ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole