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 100.
Σελίδα 9
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides B are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does ...
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which the equal sides B are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does ...
Σελίδα 10
... base FC is 4. 1. equal to the base GB , and the tri- angle AFC to the triangle AGB ; and the remaining angies of the one are equal to the remaining angles of the other , each to each , ' to which the equal sides are op- Fl posite ; viz ...
... base FC is 4. 1. equal to the base GB , and the tri- angle AFC to the triangle AGB ; and the remaining angies of the one are equal to the remaining angles of the other , each to each , ' to which the equal sides are op- Fl posite ; viz ...
Σελίδα 11
... base DC is equal to the base AB , and the triangle DBC is equal to the tri- angle ACB , the less to the greater ; which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c ...
... base DC is equal to the base AB , and the triangle DBC is equal to the tri- angle ACB , the less to the greater ; which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c ...
Σελίδα 12
... base CD are 5. 1. equal a to one another : but the an- gle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
... base CD are 5. 1. equal a to one another : but the an- gle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
Σελίδα 13
... base BC coincides with the base EF ; but the sides BA , CA do not coincide with the sides ED , FD , but have a differ- ent situation as EG , FG , then , upon the same base EF , and upon the same side of it , there can be two triangles ...
... base BC coincides with the base EF ; but the sides BA , CA do not coincide with the sides ED , FD , but have a differ- ent situation as EG , FG , then , upon the same base EF , and upon the same side of it , there can be two triangles ...
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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.