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 |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 15
... point C , D in which the circles cut one ano- ther , draw the straight lines b CА , CB to the points A , B ; ABC ... F ; from the centre B , at the distance BC , described the circle CGH , and from the centre D , at the distance DG ...
... point C , D in which the circles cut one ano- ther , draw the straight lines b CА , CB to the points A , B ; ABC ... F ; from the centre B , at the distance BC , described the circle CGH , and from the centre D , at the distance DG ...
Σελίδα 16
... point B is the centre of the circle CGH , BC is equale to BG ; and because D is the centre of the circle GKL , e 15. Def . DL is equal to DG , and DA , DB , parts of them , are equal ; f 3. Ax . therefore the remainder AL is equal to ...
... point B is the centre of the circle CGH , BC is equale to BG ; and because D is the centre of the circle GKL , e 15. Def . DL is equal to DG , and DA , DB , parts of them , are equal ; f 3. Ax . therefore the remainder AL is equal to ...
Σελίδα 17
... F For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall ...
... F For , if the triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC shall ...
Σελίδα 18
... point F , and from AE the greater , cut off AG equala to AF , the less , and join FC , GB . Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG ...
... point F , and from AE the greater , cut off AG equala to AF , the less , and join FC , GB . Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG ...
Σελίδα 20
... F that the point B be on E , and the straight line BC upon EF : the point C shall also coincide with the point F. Because BC is equal to EF ; therefore BC coinciding with 20 THE ELEMENTS.
... F that the point B be on E , and the straight line BC upon EF : the point C shall also coincide with the point F. Because BC is equal to EF ; therefore BC coinciding with 20 THE ELEMENTS.
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 parallelogram AC perpendicular point F polygon prism proposition pyramid Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar 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 28 - Any two sides of a triangle are together greater than the third side.
Σελίδα 62 - 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 28 - 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 57 - 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 26 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 163 - 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 17 - 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 189 - 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 37 - 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 178 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.