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 79.
Σελίδα 9
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides B are opposite , shall be CE equal each to each , viz . the angle ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides B are opposite , shall be CE equal each to each , viz . the angle ...
Σελίδα 12
... angle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ... BAC is equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that B E the point B be on E , and the ...
... angle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ... BAC is equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that B E the point B be on E , and the ...
Σελίδα 13
... angle BAC coincides with the angle EDF , and is equalb to it . Therefore if two triangles , & c . 8 Ax . Q.E.D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given ...
... angle BAC coincides with the angle EDF , and is equalb to it . Therefore if two triangles , & c . 8 Ax . Q.E.D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given ...
Σελίδα 18
... BAC . Bisecta AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. 4 Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle ... angle ACB ; ...
... BAC . Bisecta AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. 4 Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle ... angle ACB ; ...
Σελίδα 19
Euclides Robert Simson. these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC ... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII .
Euclides Robert Simson. these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC ... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII .
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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.