## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |

### From inside the book

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**propositions**are , which must cease to be true if this**proposition**were sup- posed to be false ? Is it not useful to know , that unless it be true , that any two sides of a triangle are greater than the third , neither could it be ... Page xvi

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**proposition**already quoted , and those that are more simple , will not be very expert in tracing its connection with those that are more complex ; and that , as he has not been careful in laying the founda- tion , he will never be ... Page 21

... are equal to one another . XI . " Two straight lines which intersect one another , cannot be both " parallel to the same straight line . "

... are equal to one another . XI . " Two straight lines which intersect one another , cannot be both " parallel to the same straight line . "

**PROPOSITION**I. PROBLEM . To describe an equilateral triangle upon OF GEOMETRY . BOOK 1 . Page 22

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**PROPOSITION**I. PROBLEM . To describe an equilateral triangle upon a given finite straight line Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the distance AB ... Page 42

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**proposition**, all the angles of these tri- angles are equal to twice as many right angles as there are triangles , that is , as there are sides of the figure ; and the same angles are equal to the angles of the figure , together with ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore