The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 16
... equal to DG , and DA , DB , parts of them , are equal ; f3 . Ax . therefore the remainder AL is equal to the remainder f BG : but it has been shown , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things ...
... equal to DG , and DA , DB , parts of them , are equal ; f3 . Ax . therefore the remainder AL is equal to the remainder f BG : but it has been shown , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things ...
Σελίδα 17
... 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 are opposite , shall be equal , each to each , viz . the angle ABC to the B ...
... 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 are opposite , shall be equal , each to each , viz . the angle ABC to the B ...
Σελίδα 18
... equal to AC , and let the straight lines AB , AC be produced to D and E ; the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . b 4. 1 . In BD take any point F , and from AE the greater , cut off ...
... equal to AC , and let the straight lines AB , AC be produced to D and E ; the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . b 4. 1 . In BD take any point F , and from AE the greater , cut off ...
Σελίδα 19
... equal to the side AC . For if AB be not equal to AC , one of them is greater than D A the other ; let AB be the greater , and from it cut a off DB a 3. 1 . equal to AC , the less , and join DC ; there- fore , because in the triangles ...
... equal to the side AC . For if AB be not equal to AC , one of them is greater than D A the other ; let AB be the greater , and from it cut a off DB a 3. 1 . equal to AC , the less , and join DC ; there- fore , because in the triangles ...
Σελίδα 20
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal a to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more ...
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal a to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 30 - Any two sides of a triangle are together greater than the third side.
Σελίδα 64 - 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 30 - 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 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 165 - 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 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Σελίδα 39 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Σελίδα 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.