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 8
... contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal ...
... contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal ...
Side 12
... contained by the two sides equal to them , of the other . Let ABC , DEF be two triangles , having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and also the base BC equal to the ...
... contained by the two sides equal to them , of the other . Let ABC , DEF be two triangles , having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and also the base BC equal to the ...
Side 22
... contained by the two sides of one of them greater than the angle contained by the two sides equal to them , of the other ; the base of that which has the greater angle shall be greater than the base of the other . Let ABC , DEF be two ...
... contained by the two sides of one of them greater than the angle contained by the two sides equal to them , of the other ; the base of that which has the greater angle shall be greater than the base of the other . Let ABC , DEF be two ...
Side 23
... contained by the sides of that which has the greater base , shall be greater than the angle contained by the sides equal to them of the other . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE ...
... contained by the sides of that which has the greater base , shall be greater than the angle contained by the sides equal to them of the other . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE ...
Side 3-11
... upon one of the sides of a triangle , be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . BOOK I. a 11. 1 . If the square described OF EUCLID . 41.
... upon one of the sides of a triangle , be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . BOOK I. a 11. 1 . If the square described OF EUCLID . 41.
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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.