## The elements of geometry: in which the principal propositions of Euclid, Archimedes, and others are demonstrated after the most easy manner. To which is added a collection of useful geometrical problems, also the Doctrine of proportion, arithmetical and geometrical, together with a general method of arguing by proportional quantities |

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ABCD angle equal arch arithmetic arithmetic progression bases and heights bisect circle whose radius circumference circumscribing common section conic surface cord cube curve surface cylinder describe diagonal divided dodecaedron drawn equal angles equal bases equilateral cone equilateral triangle external angle fame base fore frustum geometrical geometrical progression given line greater half hemisphere homologous fides ibid inscribed cone let fall mean proportional parallel planes parallelogram pentagon perp perpendicular planes AC polygon prism PROB PROP pyramid radii ratio reciprocally proportional rectangle right angle Cor right angles right line Scholium segment sides similar solid angle sphere square triangle ABC triangular prisms whence whofe whole surface

### Popular passages

Page 204 - ... the remaining ratio of the last. LET the first ratios be those of a to' b, b to С, С to d, d to e, and e to f ; and let the other ratios be those of g to h, h to k, k to l, and l to m ; also, let the ratio of a to f, which is compounded of (def.

Page 185 - If equal quantities be added to equal quantities, the sums will be equal.

Page 49 - Straight lines are said to be ' equally distant from the centre ' of a circle, when the perpendiculars drawn to them from the centre are equal.

Page 25 - As the (quart of the hyporhcnufc, or longed fide of a right-angled triangle, is equal to the fum of the fquares of the other two fides...

Page 88 - MN. 3. // a line is perpendicular to one of two parallel planes, it is perpendicular to the other plane also.

Page 48 - ... SECTION IV. — Of the Circle, and Inscribed and Circum scribed Figures. Definitions. 1. A circle is a plane figure described by a right line moving about a fixed point, as A A c about c : or it is a figure bounded by one line equidistant from a fixed point. 2. The centre of a circle is the fixed point about which the line moves, c. 3. The radius is the line that describes the circle, c A. Cor. All the radii of a circle are equal. 4. The circumference is the line described by the extreme end...

Page 92 - BG: for the same reason, in the triangles KAL, MBN, KL is equal to MN, and AL to BN : and in the triangles LAD, NBG, LA, AD are equal to NB, BG, and they contain equal angles ; therefore the base LD is equal (4.

Page 30 - Three lines drawn from the three angles of a triangle to the middle of the opposite sides, all meet in one point.

Page 111 - Becaufe every cone is the third part of a cylinder of the fame bafe and altitude, Multiply the area of its bafe by one third part of its height ; the product is the foiidity.

Page 8 - IEF=(FED)=AEF (by part 2. theo. 3.) a greater to a less, which is absurd, whence IK is not parallel ; and the like we can prove of all other lines but AB ; therefore AB is parallel to CD. QED THEO. XII.