## 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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**magnitude**, from nothing upwards ) , and yet it may in many cases be a problem of extreme difficulty to as- sign the height of such a solid , and actually to exhibit it . Now , this very supposition , that on a given base a solid of a ... Page 17

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**magnitude*** , " ( See " A Notes . ) A line is length without breadth . II . " COROLLARY . The extremities of a line are points ; and the inter- " sections of one line with another are also points . " III . " If two lines are such that ... Page 21

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**Magnitudes**which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . Χ . All right angles are equal to one another . XI . " Two straight lines ... Page 53

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**magnitudes**, signi- " fies that those**magnitudes**are to be added together , and the sign " -placed between them , signifies that the latter is to be taken away " from the former . " " The sign = signifies , that the things between which ... Page 107

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**magnitudes**of any " kind . The letters m , n , p , q , are used to denote numbers only . " 2. The sign + ( plus ) , written between two letters , that denote "**magnitudes**or numbers , signifies the sum of those**magnitudes**or " numbers ...### 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