The Elements of Euclid with Many Additional Propositions and Explanatory NotesJ. Weale, 1860 |
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Página v
... whole has , however , been entirely rewritten , and it is hoped that , in the attempt to render it less verbose , it will not be found that the chain of proof has been in any case weakened . Considerable pains have been taken to ...
... whole has , however , been entirely rewritten , and it is hoped that , in the attempt to render it less verbose , it will not be found that the chain of proof has been in any case weakened . Considerable pains have been taken to ...
Página vii
... whole science of Geometry is based upon certain simple and self - evident truths , from which , by a continuous chain of reasoning , conducted strictly in accordance with the rules of logic , the most important and complicated relations ...
... whole science of Geometry is based upon certain simple and self - evident truths , from which , by a continuous chain of reasoning , conducted strictly in accordance with the rules of logic , the most important and complicated relations ...
Página x
... whole complex idea in its full extent and generality ; that is , may perceive , at one time , every other idea which it is meant to include . While , on the other hand , the object of a definition is rather to limit the mental ...
... whole complex idea in its full extent and generality ; that is , may perceive , at one time , every other idea which it is meant to include . While , on the other hand , the object of a definition is rather to limit the mental ...
Página xi
... whole of the subject , as , " Every equiangular triangle is equilateral ; " here the quality of being equilateral is predicated of the whole of the class of equi- angular triangles ; if , however , the predicate refers only to a por ...
... whole of the subject , as , " Every equiangular triangle is equilateral ; " here the quality of being equilateral is predicated of the whole of the class of equi- angular triangles ; if , however , the predicate refers only to a por ...
Página xii
... whole of the class which the symbol Y represents . When two propositions which have the same subject and predi- cate differ in quality or quantity , or both , they are said to be If they differ in both quality and quan tity they xii ...
... whole of the class which the symbol Y represents . When two propositions which have the same subject and predi- cate differ in quality or quantity , or both , they are said to be If they differ in both quality and quan tity they xii ...
Otras ediciones - Ver todas
The Elements of Euclid: With Many Additional Propositions, & Explanatory ... Euclid Sin vista previa disponible - 2023 |
The Elements of Euclid: With Many Additional Propositions, and Explanatory ... Euclid Sin vista previa disponible - 2013 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.
Página 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...