The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth ... Also the Book of Euclid's Data, in Like Manner CorrectedWingrave and Collingwood, 1816 - 528 sider |
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Side 8
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw the straight line AD equal to C ; and from the centre A , and at the di- b3 Post . stance AD , describeb the circle DEF ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw the straight line AD equal to C ; and from the centre A , and at the di- b3 Post . stance AD , describeb the circle DEF ...
Side 11
... greater than the other : Let AB be the greater ; and from it cuta 3. 1 . off DB equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both the two sides , DB , BC ...
... greater than the other : Let AB be the greater ; and from it cuta 3. 1 . off DB equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both the two sides , DB , BC ...
Side 12
... greater than BCD ; much more then is the angle BDC greater than the angle BCD Again , because CB is equal to DB , the angle BDC A is equal to the angle BCD ; but BDC has been proved to be greater than the same BCD ; which is impossible ...
... greater than BCD ; much more then is the angle BDC greater than the angle BCD Again , because CB is equal to DB , the angle BDC A is equal to the angle BCD ; but BDC has been proved to be greater than the same BCD ; which is impossible ...
Side 18
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : In the same manner , if the side BC be bisected , it may be 15. 1. demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC ...
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : In the same manner , if the side BC be bisected , it may be 15. 1. demonstrated that the angle BCG , that is , the angle ACD , is greater than the angle ABC ...
Side 19
... greater than the angles ABC , ACB ; but ACD , ACB are together equal to two right angles ; therefore the angles ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater ...
... greater than the angles ABC , ACB ; but ACD , ACB are together equal to two right angles ; therefore the angles ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater ...
Almindelige termer og sætninger
ABC is given ABCD AC is equal altitude angle ABC angle BAC base BC bisected Book XI centre circle ABC circumference common logarithm 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 logarithm multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition Q.E.D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of BC straight line AB straight line BC tangent THEOR third triangle ABC vertex wherefore
Populære passager
Side 41 - 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.
Side 180 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 166 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides. DH Let BC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Side 2 - A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles.
Side 105 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Side 79 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 1 - A straight line is that which lies evenly between its extreme points.
Side 149 - 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.
Side 23 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 83 - Wherefore from the given circle ABC has been cut off the segment BAC, containing an angle equal to the given angle DQEP PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the...
Bibliografiske oplysninger
| Titel | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth ... Also the Book of Euclid's Data, in Like Manner Corrected |
| Forfatter | Euclides |
| Redaktør | Robert Simson |
| Udgave | 17 |
| Udgiver | Wingrave and Collingwood, 1816 |
| Oprindeligt fra | Complutense-universitetet i Madrid |
| Digitaliseret | 20. maj 2008 |
| Længde | 528 sider |
| Eksporter henvisning | BiBTeX EndNote RefMan |