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 Seiten |
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Seite 118
... proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . ' VII ... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI ...
... proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . ' VII ... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI ...
Seite 119
... proportionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is in- ferred , that the first has the same ratio to the third , which the second has ...
... proportionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is in- ferred , that the first has the same ratio to the third , which the second has ...
Seite 120
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others : Of this there are the two following kinds , which arise ...
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others : Of this there are the two following kinds , which arise ...
Seite 127
... proportionals , they are propor- tionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A and C any ...
... proportionals , they are propor- tionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A and C any ...
Seite 127
... proportionals , they are propor- tionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A and C any ...
... proportionals , they are propor- tionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A and C any ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 81 - The angles in the same segment of a circle are equal to one another.
Seite 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 22 - ANY two angles of a triangle are together less than two right angles.
Seite 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Seite 24 - Any two sides of a triangle are together greater than the third side.