The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; 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 CorrectedDesilver, 1829 - 516 σελίδες |
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Αποτελέσματα 1 - 5 από τα 43.
Σελίδα 117
... equi- multiples whatsoever of the second and fourth ; if the multi- ple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or , if the multiple of the first be equal to that ...
... equi- multiples whatsoever of the second and fourth ; if the multi- ple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or , if the multiple of the first be equal to that ...
Σελίδα 118
... equimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said ...
... equimultiples of four magnitudes ( taken as in the fifth definition ) the multiple of the first is greater than that of the second , but the multiple of the third is not greater than the multiple of the fourth ; then the first is said ...
Σελίδα 120
... EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . * 4 Prop . lib . 2. Archimedis de sphæra et cylindro . II . Those magnitudes of which the same , or 120 BOOK V. THE ELEMENTS OF EUCLID .
... EQUIMULTIPLES of the same , or of equal magnitudes , are equal to one another . * 4 Prop . lib . 2. Archimedis de sphæra et cylindro . II . Those magnitudes of which the same , or 120 BOOK V. THE ELEMENTS OF EUCLID .
Σελίδα 121
... equimultiples of as many , each of each ; what multiple soever any one of them is of its part , the same multiple shall all the first magni- tudes be of all the other . Let any number of magnitudes AB , CD be equimultiples of as many ...
... equimultiples of as many , each of each ; what multiple soever any one of them is of its part , the same multiple shall all the first magni- tudes be of all the other . Let any number of magnitudes AB , CD be equimultiples of as many ...
Σελίδα 123
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first , be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimultiples EF ...
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first , be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let the equimultiples EF ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram 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 AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 81 - The angles in the same segment of a circle are equal to one another.
Σελίδα 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 33 - 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 sides.
Σελίδα 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Σελίδα 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.
Σελίδα 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Σελίδα 24 - Any two sides of a triangle are together greater than the third side.