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 5
... halves of the same , are equal to one an- other . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . BOOK I. IX . The whole is greater than its OF EUCLID . 5.
... halves of the same , are equal to one an- other . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . BOOK I. IX . The whole is greater than its OF EUCLID . 5.
Página 6
Euclides Robert Simson. BOOK I. IX . The whole is greater than its part . " X. Two straight lines cannot inclose a space . XI . All right angles are equal to one another . XII . " If a straight line meets two straight lines , so as to ...
Euclides Robert Simson. BOOK I. IX . The whole is greater than its part . " X. Two straight lines cannot inclose a space . XI . All right angles are equal to one another . XII . " If a straight line meets two straight lines , so as to ...
Página 9
... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF ...
... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF ...
Página 10
... whole AF , is equal to the whole C B A C G E AG , of which the parts AB , AC , are equal ; .the remainder 3 Ax . BF shall be equal to the remainder CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to ...
... whole AF , is equal to the whole C B A C G E AG , of which the parts AB , AC , are equal ; .the remainder 3 Ax . BF shall be equal to the remainder CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to ...
Página 29
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equale to ...
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equale to ...
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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.