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 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 51.
Σελίδα
... Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppressing others , and mixing his own with Euclid's Demonstrations , has changed more things to the worse ...
... Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppressing others , and mixing his own with Euclid's Demonstrations , has changed more things to the worse ...
Σελίδα 74
... Greek text , and translations from it , the angle of ' the semicircle is said to be greater than any acute rectili- ' neal angle , and the remaining angle less than any rectiii- ' neal angle . ' Q.E.D. COR . From this it is manifest ...
... Greek text , and translations from it , the angle of ' the semicircle is said to be greater than any acute rectili- ' neal angle , and the remaining angle less than any rectiii- ' neal angle . ' Q.E.D. COR . From this it is manifest ...
Σελίδα 85
... of the greater segment ABC falls without the right angle CAB ; but the circumference of the less segment ADC falls with- in the right angle CAF . And this is all that is meant , e BOOK III . when in the Greek text , and OF EUCLID . 85.
... of the greater segment ABC falls without the right angle CAB ; but the circumference of the less segment ADC falls with- in the right angle CAF . And this is all that is meant , e BOOK III . when in the Greek text , and OF EUCLID . 85.
Σελίδα 86
... Greek text , and the translations from it , the ' angle of the greater segment is said to be greater , and the ' angle of the less segment is said to be less , than a right ' angle . ' COR . From this it is manifest , that if one angle ...
... Greek text , and the translations from it , the ' angle of the greater segment is said to be greater , and the ' angle of the less segment is said to be less , than a right ' angle . ' COR . From this it is manifest , that if one angle ...
Σελίδα 265
... Greek , because the pyramid , in what follows , is supposed to be circumscribed about the cone , and so must have the same vertex . And the same change is made in some places following . b Book XII . ments upon EO , OF , FP OF EUCLID . 265.
... Greek , because the pyramid , in what follows , is supposed to be circumscribed about the cone , and so must have the same vertex . And the same change is made in some places following . b Book XII . ments upon EO , OF , FP OF EUCLID . 265.
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 1 - A straight line is that which lies evenly between its extreme points.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...