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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Αποτελέσματα 1 - 5 από τα 49.
Σελίδα 305
... given in that book " as in this But indeed there is scarce any need of it in ... species of compound ra- tio : But Theon has made it the 5th def . of B. 6 ... given , but they retain also Theon's , which they ought to have left out of the ...
... given in that book " as in this But indeed there is scarce any need of it in ... species of compound ra- tio : But Theon has made it the 5th def . of B. 6 ... given , but they retain also Theon's , which they ought to have left out of the ...
Σελίδα 359
... species , which have each of their angles given , and the ratios of their sides given . IV . Points , lines , and spaces , are said to be given in position , which have always the same situation , and which are either actually exhibited ...
... species , which have each of their angles given , and the ratios of their sides given . IV . Points , lines , and spaces , are said to be given in position , which have always the same situation , and which are either actually exhibited ...
Σελίδα 388
... given : But as LM to MN , so is GH to HK ; wherefore the ratio of GH to HK is given . $ 9 . PROP . XLII . See N. IF each of the sides of a triangle be given in`mag- nitude , the triangle is given in species . * 22. 1 . Let each of the ...
... given : But as LM to MN , so is GH to HK ; wherefore the ratio of GH to HK is given . $ 9 . PROP . XLII . See N. IF each of the sides of a triangle be given in`mag- nitude , the triangle is given in species . * 22. 1 . Let each of the ...
Σελίδα 389
... given , wherefore each of those at the points D , E , F , is given : And because the straight line FD is drawn to ... species . с e 29 Dat . 42 Dat . S4.6 . { 1 Def . 6 . PROP . XLIV . If one of the angles of a triangle be given , and if ...
... given , wherefore each of those at the points D , E , F , is given : And because the straight line FD is drawn to ... species . с e 29 Dat . 42 Dat . S4.6 . { 1 Def . 6 . PROP . XLIV . If one of the angles of a triangle be given , and if ...
Σελίδα 390
... given in species . Let the sides of the triangle ABC have given ratios to one another , the triangle ABC is given in species . Take a straight line D given in magnitude ; and because the ratio of AB to BC is given , make the ratio of D ...
... given in species . Let the sides of the triangle ABC have given ratios to one another , the triangle ABC is given in species . Take a straight line D given in magnitude ; and because the ratio of AB to BC is given , make the ratio of D ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 16 - Any two sides of a triangle are together greater than the third side.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.