The Elements of Euclid; viz. the first six books, together with the eleventh and twelfth. Also the book of Euclid's Data. By R. Simson. To which is added, A treatise on the construction of the trigonometrical canon [by J. Christison] and A concise account of logarithms [by A. Robertson].1834 |
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Results 6-10 of 18
Page 216
... prism GHKLMN . Complete the solids AX , GO : and because the parallelo- gram AF is double of the triangle GHK , and ... prism ABCDEF is half * of the solid AX ; and the prism GHKLMN half of the solid GO : therefore the prism ABCDEF ...
... prism GHKLMN . Complete the solids AX , GO : and because the parallelo- gram AF is double of the triangle GHK , and ... prism ABCDEF is half * of the solid AX ; and the prism GHKLMN half of the solid GO : therefore the prism ABCDEF ...
Page 221
... prisms which together are greater than half of the whole pyramid . -100 D Let there be a pyramid , of which the base is the triangle ABC , and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyramids ...
... prisms which together are greater than half of the whole pyramid . -100 D Let there be a pyramid , of which the base is the triangle ABC , and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyramids ...
Page 222
... prisms of the same altitude , of which one has a parallelogram for its base , and the other a triangle that is half of the parallelogram , these prisms are equal * to one another ; therefore the prism having the parallelogram EBFG ...
... prisms of the same altitude , of which one has a parallelogram for its base , and the other a triangle that is half of the parallelogram , these prisms are equal * to one another ; therefore the prism having the parallelogram EBFG ...
Page 223
... prism having the triangle GFC for its base , and the triangle HKL opposite to it ; for they are of the same altitude , because they are between the pa- rallel * planes ABC , HKL : and it is manifest that each of 15.11 . these prisms is ...
... prism having the triangle GFC for its base , and the triangle HKL opposite to it ; for they are of the same altitude , because they are between the pa- rallel * planes ABC , HKL : and it is manifest that each of 15.11 . these prisms is ...
Page 224
... prism having the triangle LXC for its base , and OMN the triangle opposite to it , to the prism of which the base is the triangle RVF , and the opposite triangle STY : and because the two prisms in the pyramid ABCG are equal to one ...
... prism having the triangle LXC for its base , and OMN the triangle opposite to it , to the prism of which the base is the triangle RVF , and the opposite triangle STY : and because the two prisms in the pyramid ABCG are equal to one ...
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Common terms and phrases
ABC is given altitude angle ABC angle BAC base BC BC is equal bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC logarithm multiple parallel parallelogram perpendicular plane angles polygon prism Prop proportionals Q. E. D. PROPOSITION radius ratio of AE rectangle contained rectilineal figure remaining angle right angles segment shewn sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR three plane angles tiple triangle ABC vertex wherefore
Popular passages
Page 32 - To a given straight line, to apply a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle...
Page 138 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 39 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Page 22 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Page 41 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Page 5 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Page 38 - IF a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided...
Page 262 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Page 89 - PBOR. —To describe an isosceles triangle, having each of the angles at the base, double of the third angle. Take any straight...
Page 165 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.