The Elements of Euclid with Many Additional Propositions and Explanatory NotesJ. Weale, 1860 |
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Resultat 1-5 av 85
Side xviii
... contained under it . Now it is only to moods in the first figure that this principle can be directly and at once applied , and therefore this figure has been termed perfect , and the other figures which require to be reduced to the ...
... contained under it . Now it is only to moods in the first figure that this principle can be directly and at once applied , and therefore this figure has been termed perfect , and the other figures which require to be reduced to the ...
Side 4
... contained by the arc and its chord is termed a segment . The space contained by two arcs of circles of different radii is termed a lune , as GHI . B 18. A RECTILINEAL FIGURE is a plane surface , bounded on all sides by straight lines ...
... contained by the arc and its chord is termed a segment . The space contained by two arcs of circles of different radii is termed a lune , as GHI . B 18. A RECTILINEAL FIGURE is a plane surface , bounded on all sides by straight lines ...
Side 5
... contained under four lines , two of which , AB and BC , are equal the other two , CD and AD , it is designated as the rectangle under those two lines ; thus the rectangle ABCD would be termed the rectangle under AB and BC . 28. A SQUARE ...
... contained under four lines , two of which , AB and BC , are equal the other two , CD and AD , it is designated as the rectangle under those two lines ; thus the rectangle ABCD would be termed the rectangle under AB and BC . 28. A SQUARE ...
Side 52
... contained by any two of the straight lines which contain one of the right angles . SCHOLIUM . As already explained in the scholium to the twenty - seventh definition in the former Book , a rectangle is designated as the rectangle under ...
... contained by any two of the straight lines which contain one of the right angles . SCHOLIUM . As already explained in the scholium to the twenty - seventh definition in the former Book , a rectangle is designated as the rectangle under ...
Side 54
... contained in its length . Thus , if the original unit had been a foot , and on applying it to the given line we had found it contained four times , together with a remainder less than a foot ; but that , on dividing the unit into twelve ...
... contained in its length . Thus , if the original unit had been a foot , and on applying it to the given line we had found it contained four times , together with a remainder less than a foot ; but that , on dividing the unit into twelve ...
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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...