The Elements of Euclid with Many Additional Propositions and Explanatory NotesJ. Weale, 1860 |
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Side vii
... hypotheses and theories are unknown , to which experiment and experience have rendered no aid , and whose conclusions are certain and immutable . However much the rules of logic may assist in obtaining true conclusions in the ...
... hypotheses and theories are unknown , to which experiment and experience have rendered no aid , and whose conclusions are certain and immutable . However much the rules of logic may assist in obtaining true conclusions in the ...
Side 16
... hypotheses and one predicate , if another theorem be framed having one of those hypotheses for its predicate and the predicate of the first as one of its hypotheses , the two theorems are the converse of each other ; and it is in this ...
... hypotheses and one predicate , if another theorem be framed having one of those hypotheses for its predicate and the predicate of the first as one of its hypotheses , the two theorems are the converse of each other ; and it is in this ...
Side 84
... hypotheses for its predicate and the former predicate for one of its hypotheses , the second theorem will be the converse of the first ; and therefore , in fact , as many converse propo- sitions might be framed as the first theorem ...
... hypotheses for its predicate and the former predicate for one of its hypotheses , the second theorem will be the converse of the first ; and therefore , in fact , as many converse propo- sitions might be framed as the first theorem ...
Side 119
... HYPOTHESES . If two lines be straight If a straight line standing upon another forms angles with it . If two straight lines meet another straight line at the same point and on opposite sides , and make the ad- jacent angles with it to ...
... HYPOTHESES . If two lines be straight If a straight line standing upon another forms angles with it . If two straight lines meet another straight line at the same point and on opposite sides , and make the ad- jacent angles with it to ...
Side 120
... HYPOTHESES . If a straight line intersect two other straight lines , | both in the same plane , And form alternate angles equal to each other , Or form an external angle equal to the internal and opposite angle upon the same side of the ...
... HYPOTHESES . If a straight line intersect two other straight lines , | both in the same plane , And form alternate angles equal to each other , Or form an external angle equal to the internal and opposite angle upon the same side of the ...
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Vanlige uttrykk og setninger
AC is equal altitude angle ABC bisected circle ABCD circumference cone CONSTRUCTION contained COROLLARY cylinder DEMONSTRATION diameter divided double draw duplicate ratio EFGH equal angles equal in area equiangular equilateral equimultiples Euclid external angle fore fourth given line given rectilineal given straight line gnomon greater ratio homologous sides Hypoth HYPOTHESES inscribed join less line AC lines be drawn meet multiple opposite angle parallel parallelogram perpendicular polygon prism proposition pyramid ABCG pyramid DEFH rectangle rectilineal figure remaining angle right angles SCHOLIA SCHOLIUM segment side AC solid angle solid CD solid parallelopipeds sphere square on AB square on AC syllogism THEOREM THEOREM.-If third three plane angles tiple triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 107 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Side 85 - ... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another.
Side 18 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding...
Side 82 - From the point A draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the triangle ABC, viz. to BC ; as CD is to DA, so is (2.
Side 111 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 116 - ... plane, from a given point above it. Let A be the given point above the plane BH; it is required to draw from the point A a straight line perpendicular to the plane BH.
Side 115 - For the same reason, CD is likewise at right angles to the plane HGK. Therefore AB, CD are each of them at right angles to the plane HGK.
Side 49 - IF magnitudes, taken jointly, be proportionals, they shall also be proportionals when taken separately ; that is, if two magnitudes together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same ratio which the remaining one of the last two has to the other of these. Let AB, BE, CD...
Side 32 - 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.
Side 34 - Take of B and D any equimultiples whatever E and F; and of A and C any equimultiples whatever G and H. First, let E be greater than G, then G is less than E: and because A is to B, as C is to D, (hyp.) and of A and C...