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 Seiten |
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Seite 287
... EDITION DIFFERS FROM THE GREEK TEXT ; AND THE REASONS OF THE ALTERATIONS WHICH HAVE BEEN MADE . AS ALSO , OBSERVATIONS ON SOME OF THE PROPOSITIONS . BY ROBERT SIMSON , M. D. EMERITUS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW ...
... EDITION DIFFERS FROM THE GREEK TEXT ; AND THE REASONS OF THE ALTERATIONS WHICH HAVE BEEN MADE . AS ALSO , OBSERVATIONS ON SOME OF THE PROPOSITIONS . BY ROBERT SIMSON , M. D. EMERITUS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW ...
Seite 294
... edition of his Ele- ments of Geometry , printed anno 1760 , observes in his notes , that it El ought to have been shown , that the point F falls below the line EG . This probably Euclid omitted , as it is very easy to perceive , that DG ...
... edition of his Ele- ments of Geometry , printed anno 1760 , observes in his notes , that it El ought to have been shown , that the point F falls below the line EG . This probably Euclid omitted , as it is very easy to perceive , that DG ...
Seite 307
... in his edition of Euclid , after he had given the other which he blames . He says , he would not leave it out , because it was fine , and might C C B D BOOK V. sharpen one's genius to invent others like it X 2 NOTES . 807.
... in his edition of Euclid , after he had given the other which he blames . He says , he would not leave it out , because it was fine , and might C C B D BOOK V. sharpen one's genius to invent others like it X 2 NOTES . 807.
Seite 308
... edition of the 5th book ; and he might as well have left out the other , as also the fifth proposition , for the The demonstration of the other case is now added , because both of them , as also the 5th , proposition , are necessary to ...
... edition of the 5th book ; and he might as well have left out the other , as also the fifth proposition , for the The demonstration of the other case is now added , because both of them , as also the 5th , proposition , are necessary to ...
Seite 309
... edition , and is followed by Herigon in Schol . 1. Prop . 4. B. 5 , as if there was any na- ture of proportionals antecedent to that which is to be de- rived and understood from the definition of them : And indeed , though it is very ...
... edition , and is followed by Herigon in Schol . 1. Prop . 4. B. 5 , as if there was any na- ture of proportionals antecedent to that which is to be de- rived and understood from the definition of them : And indeed , though it is very ...
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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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 1 - A straight line is that which lies evenly between its extreme points.
Seite 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.
Seite 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.
Seite 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...