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 61
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B any two points in the cir- cumference ; the straight line drawn from A to B shall fall within the ...
... taken in the circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A , B any two points in the cir- cumference ; the straight line drawn from A to B shall fall within the ...
Page 65
... taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and ...
... taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and ...
Page 66
... taken , & c . Q. E. D. PROP . VIII . THEOR . If any point be taken without a circle , and straight lines be drawn from it to the circumference , where- of one passes through the centre ; of those which fall upon the concave ...
... taken , & c . Q. E. D. PROP . VIII . THEOR . If any point be taken without a circle , and straight lines be drawn from it to the circumference , where- of one passes through the centre ; of those which fall upon the concave ...
Page 68
... taken within a circle , from which there fall more than two equal straight lines to the cir- cumference , that point is the centre of the circle . Let the point D be taken within the circle ABC , from which to the circumference there ...
... taken within a circle , from which there fall more than two equal straight lines to the cir- cumference , that point is the centre of the circle . Let the point D be taken within the circle ABC , from which to the circumference there ...
Page 92
... taken without the circle ABC , and from it let two straight lines DCA and DB be drawn , of which DCA cuts the circle , and DB meets it ; if the rect- anglè AD , DC be equal to the square of DB , DB touches the circle . Draw a the ...
... taken without the circle ABC , and from it let two straight lines DCA and DB be drawn , of which DCA cuts the circle , and DB meets it ; if the rect- anglè AD , DC be equal to the square of DB , DB touches the circle . Draw a 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.