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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Side 31
... third angle of the one to the third angle of the other " , viz . the side AB to the side CD , and 26. 1 . AC to BD , and the angle BAC equal to the angle BDC : And because the angle ABC is equal to the angle BCD , and the angle CBD to ...
... third angle of the one to the third angle of the other " , viz . the side AB to the side CD , and 26. 1 . AC to BD , and the angle BAC equal to the angle BDC : And because the angle ABC is equal to the angle BCD , and the angle CBD to ...
Side 65
... third , BE , EF , are greater than BF ; 20. 1 . but AE is equal to EB ; there- fore AE , EF , that is AF , is greater than BF : Again , be- cause BE is equal to CE , and FE common to the triangles BEF , CEF , the two sides BE , EF are ...
... third , BE , EF , are greater than BF ; 20. 1 . but AE is equal to EB ; there- fore AE , EF , that is AF , is greater than BF : Again , be- cause BE is equal to CE , and FE common to the triangles BEF , CEF , the two sides BE , EF are ...
Side 102
... third angle . Take any straight line AB , and dividea it in the point C , so that the rectangle AB , BC be equal to the square of CA ; and from the centre A , at the distance AB , describe the 1. 4. circle BDE , in which placeb the ...
... third angle . Take any straight line AB , and dividea it in the point C , so that the rectangle AB , BC be equal to the square of CA ; and from the centre A , at the distance AB , describe the 1. 4. circle BDE , in which placeb the ...
Side 103
... third angle . Which was to be done . PROP . XI . PROB . To inscribe an equilateral and equiangular penta- gon in a given circle . Let ABCDE be the given circle ; it is required to in- scribe an equilateral and equiangular pentagon in ...
... third angle . Which was to be done . PROP . XI . PROB . To inscribe an equilateral and equiangular penta- gon in a given circle . Let ABCDE be the given circle ; it is required to in- scribe an equilateral and equiangular pentagon in ...
Side 105
... third angle to the third angle : There- fore the straight line KC is equal to CL , and the angle FKC to the angle FLC : And because KC is equal to CL , KL is double of KC ; In the same manner it may be shown that HK is double of BK ...
... third angle to the third angle : There- fore the straight line KC is equal to CL , and the angle FKC to the angle FLC : And because KC is equal to CL , KL is double of KC ; In the same manner it may be shown that HK is double of BK ...
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The Elements of Euclid; viz. the first six books, together with the eleventh ... Euclides Uten tilgangsbegrensning - 1834 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 16 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 159 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.