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 |
From inside the book
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Page 7
... draw a straight line equal . to a given straight line . Let A be the given point , and BC the given straight line ; it is required to draw from the point A a straight line equal to BC . From the point A to B drawa the straight line AB ...
... draw a straight line equal . to a given straight line . Let A be the given point , and BC the given straight line ; it is required to draw from the point A a straight line equal to BC . From the point A to B drawa the straight line AB ...
Page 14
... draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in it ; it is required to draw a straight line from the point C at right angles to AB ...
... draw a straight line at right angles to a given straight line , from a given point in the same . Let AB be a given straight line , and C a point given in it ; it is required to draw a straight line from the point C at right angles to AB ...
Page 15
... draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be pro- duced to any length both ways , and let C be a point with- out it ...
... draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be pro- duced to any length both ways , and let C be a point with- out it ...
Page 29
... drawn through the given point27.1 . A parallel to the given straight line BC . Which was to be done .. PROP . XXXII ... draw CE parallela to the straight line AB ; and because AB is parallel to CE , and AC meets them , the alternate an ...
... drawn through the given point27.1 . A parallel to the given straight line BC . Which was to be done .. PROP . XXXII ... draw CE parallela to the straight line AB ; and because AB is parallel to CE , and AC meets them , the alternate an ...
Page 33
... draw BE pa- to the points E , F , and rallel to CA ; and through E B F b 31. 1 . C draw CF parallel to BD ; therefore each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equalb 35. 1 . to DBCF , because they are upon the ...
... draw BE pa- to the points E , F , and rallel to CA ; and through E B F b 31. 1 . C draw CF parallel to BD ; therefore each of the figures EBCA , DBCF is a parallelogram ; and EBCA is equalb 35. 1 . to DBCF , because they are upon the ...
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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.