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].1814 |
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Page 78
... circle , let BAD , BED be angles in it ; these also are equal to one ano- ther : Draw AF to the centre , and produce ... ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right ...
... circle , let BAD , BED be angles in it ; these also are equal to one ano- ther : Draw AF to the centre , and produce ... ABCD be a quadrilateral figure in the circle ABCD ; any two of its opposite angles are together equal to two right ...
Page 85
... ABCD be a circle , of which the diameter is BC , and centre E ; and draw CA , dividing the circle into the segments ABC , ADC , and join BA , AD , DC ; the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC ...
... ABCD be a circle , of which the diameter is BC , and centre E ; and draw CA , dividing the circle into the segments ABC , ADC , and join BA , AD , DC ; the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC ...
Page 86
... circle ABCD in B , and from the point B let the straight line BD be drawn , cutting the circle : The angles which BD makes with the touching line EF shall be equal to the angles in the alter- nate segments of the circle : that is , the ...
... circle ABCD in B , and from the point B let the straight line BD be drawn , cutting the circle : The angles which BD makes with the touching line EF shall be equal to the angles in the alter- nate segments of the circle : that is , the ...
Page 89
... circle cut one an- See N. other , the rectangle contained by the segments of one of them , is equal to the rectangle contained by the segments of the other . Let the two straight lines AC , BD , within the circle . ABCD , cut one ...
... circle cut one an- See N. other , the rectangle contained by the segments of one of them , is equal to the rectangle contained by the segments of the other . Let the two straight lines AC , BD , within the circle . ABCD , cut one ...
Page 99
... circle . Let ABCD be the given circle ; it is required to inscribe a square in ABCD . Draw the diameters AC , BD , at right angles to one an- other , and join AB , BC , CD , DA ; because BE is equal to ED , for E is the centre , and ...
... circle . Let ABCD be the given circle ; it is required to inscribe a square in ABCD . Draw the diameters AC , BD , at right angles to one an- other , and join AB , BC , CD , DA ; because BE is equal to ED , for E is the centre , and ...
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Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected BOOK XI centre circle ABCD circumference common logarithm cone cylinder demonstrated described diameter drawn equal angles equiangular equimultiples Euclid 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 meet multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Popular passages
Page 3-7 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 16 - Any two sides of a triangle are together greater than the third side.
Page 26 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 16 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Page 304 - 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 4 - DL is equal to DG, and DA, DB, parts of them, are equal ; therefore the remainder AL is equal to the remainder (3. Ax.) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC.
Page 147 - 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 3-16 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Page 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.