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 320
... Arch . de Sph . et Cyl . and as the moderns explain that term ) is the number which multiplied into the consequent term of a ratio produces the antecedent , or , which is the same thing , the number which arises by dividing the ante ...
... Arch . de Sph . et Cyl . and as the moderns explain that term ) is the number which multiplied into the consequent term of a ratio produces the antecedent , or , which is the same thing , the number which arises by dividing the ante ...
Page 473
... arch AC to the whole circumference . Produce AB till it meet the circle again in F , and through B draw DE perpendicular to AB , meeting the cir- cle in D , E. By 33. 6. Elem . the angle ABC is to a right angle ABD , as the arch AC to the ...
... arch AC to the whole circumference . Produce AB till it meet the circle again in F , and through B draw DE perpendicular to AB , meeting the cir- cle in D , E. By 33. 6. Elem . the angle ABC is to a right angle ABD , as the arch AC to the ...
Page 474
... arch , of so many degrees , minutes , seconds , & c . is the angle , of which that arch is the measure , said to be . COR . Whatever be the radius of the circle of which the measure of a given angle is an arch , that arch will con- tain ...
... arch , of so many degrees , minutes , seconds , & c . is the angle , of which that arch is the measure , said to be . COR . Whatever be the radius of the circle of which the measure of a given angle is an arch , that arch will con- tain ...
Page 475
... arch which is the measure of any given angle ABC , is to the sine , versed sine , tangent , and se- cant , of any other arch which is the measure of the same angle , as the radius of the first is to the radius of the second . Let AC ...
... arch which is the measure of any given angle ABC , is to the sine , versed sine , tangent , and se- cant , of any other arch which is the measure of the same angle , as the radius of the first is to the radius of the second . Let AC ...
Page 504
... arches of three great cir- cles , each of which is less than a semicircle . IV . A spherical angle is that on which ... arch DC will be a quadrant . Let the great circle CD meet ABC again in A , and let AC be the common section of the ...
... arches of three great cir- cles , each of which is less than a semicircle . IV . A spherical angle is that on which ... arch DC will be a quadrant . Let the great circle CD meet ABC again in A , and let AC be the common section of 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.