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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Página 307
... given the method of doing : For this reason , we have changed the construction to one , which , without doubt , is Euclid's , in which no- thing is required but to add a magnitude to it- self a certain number of times ; and this is to ...
... given the method of doing : For this reason , we have changed the construction to one , which , without doubt , is Euclid's , in which no- thing is required but to add a magnitude to it- self a certain number of times ; and this is to ...
Página 312
... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude ...
... given the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude ...
Página 330
... given rectangle , it is required to apply a rectangle to AB equal to C , D ... given straight line AB the rectangle AP has been applied equal to the given ... magnitude of it being likewise given , to find its sides . And the 4th ...
... given rectangle , it is required to apply a rectangle to AB equal to C , D ... given straight line AB the rectangle AP has been applied equal to the given ... magnitude of it being likewise given , to find its sides . And the 4th ...
Página 333
... magnitude , that are neither similar nor equal , as shall be demonstrated after the notes on the 10th definition : Upon this account it was necessary to amend the definition of similar solid figures , and so place the definition of a ...
... magnitude , that are neither similar nor equal , as shall be demonstrated after the notes on the 10th definition : Upon this account it was necessary to amend the definition of similar solid figures , and so place the definition of a ...
Página 336
... magnitude D which is less than A , B , C , to- gether , but greater than the excess of A above B and C : Then B , C , D , together are greater than A ; and because A is greater than either B or C , much more will A and D , together with ...
... magnitude D which is less than A , B , C , to- gether , but greater than the excess of A above B and C : Then B , C , D , together are greater than A ; and because A is greater than either B or C , much more will A and D , together with ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 16 - Any two sides of a triangle are together greater than the third side.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.