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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Common terms and phrases
AB² ABCD AC² AD² AG² alfo alſo arch bafes and heights baſe bifect circle whofe radius circumfcribing circumference common fection compaffes confequently cube curve furface cylinder decagon defcribe diagonal diameter diftance divided dodecaedron draw drawn equal angles equal bafes fame bafe fecond fector fegment fides figure fimilar fince firft fmall folid angle fore fphere fquare fuppofed geometrical given line greater hemifphere homologous fides hypothenufe ibid infcribed interfect laft lefs mean proportional muſt oppofite angles oppofite fide parallel parallelogram pentagon perp perpendicular plane polygon prifm PROB progreffion PROP pyramid quantities radii ratio reafon rectangle refpectively right angles right line SCHOLIUM thefe theſe thofe trapezium triangle ABC whence whole furface whoſe
Popular passages
Page 202 - ... 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 183 - 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 23 - 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 28 - 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.