Skeleton propositions &c. of Euclid, books i and ii, with references, by H. Green, Volumen11868 |
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Página xx
... contain a greater angle . CON . Pst . 2 . DEM . P. 20. Ax . 4. P. 16 . EXP . 1 | Hyp . 2 Concl . 1 . " " CON . 1 Pst . 2 . DEM . 1 P. 20 . 2 Add . 3 Ax . 4 . 2 . USE . 4 P. 20 . 5 Add . 6 Ax . 4 . 7 D. 3 . 8 a fort . 9 P. 16 . 10 P. 16 ...
... contain a greater angle . CON . Pst . 2 . DEM . P. 20. Ax . 4. P. 16 . EXP . 1 | Hyp . 2 Concl . 1 . " " CON . 1 Pst . 2 . DEM . 1 P. 20 . 2 Add . 3 Ax . 4 . 2 . USE . 4 P. 20 . 5 Add . 6 Ax . 4 . 7 D. 3 . 8 a fort . 9 P. 16 . 10 P. 16 ...
Página xxiii
... angle contained by the two sides of the one greater than the angle contained by the two sides of the other , the base of that which has the greater angle shall be greater than the base of the other . CON . P. 23. 3. Pst . 1 . DEM . P. 4 ...
... angle contained by the two sides of the one greater than the angle contained by the two sides of the other , the base of that which has the greater angle shall be greater than the base of the other . CON . P. 23. 3. Pst . 1 . DEM . P. 4 ...
Página xxiv
... angle contained by the sides of the one whic the greater base shall be greater than the angle contained by the sides equal to them of the other . DEM . P. 4. 24 . EXP . 1 Hyp . 1 . 2 " " 2 . 3 Concl . DEM . 1 Sup , 2 " " 3 H. P. 4 . 4 ...
... angle contained by the sides of the one whic the greater base shall be greater than the angle contained by the sides equal to them of the other . DEM . P. 4. 24 . EXP . 1 Hyp . 1 . 2 " " 2 . 3 Concl . DEM . 1 Sup , 2 " " 3 H. P. 4 . 4 ...
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... angle , is equal to the squares described upon the sides containing the rt . angle . CON . P. 46. 31. Pst . 1 . DEM . Def . 30. P. 14. Ax . 1. 2. P. 4. 41. Ax . 6 . EXP . 1 | Hyp . 2 Concl . CON 74 PROP . XLVI . XLVII .
... angle , is equal to the squares described upon the sides containing the rt . angle . CON . P. 46. 31. Pst . 1 . DEM . Def . 30. P. 14. Ax . 1. 2. P. 4. 41. Ax . 6 . EXP . 1 | Hyp . 2 Concl . CON 74 PROP . XLVI . XLVII .
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... angle contained by the two sides is a rt . angle . CON . P. 11. 3. Pst . 1 . DEM . Ax . 2. P. 47. Ax . 1. P. 8 . EXP . 1 | Hyp . 2 Concl . CON . 1 P. 11 . 2 P. 3. Pst . 1 . DEM . 1 C. 2 . 2 Add . 3 Ax . 2 . 4 C. 1 . 5 P. 47 . 6 Hyp . 7 ...
... angle contained by the two sides is a rt . angle . CON . P. 11. 3. Pst . 1 . DEM . Ax . 2. P. 47. Ax . 1. P. 8 . EXP . 1 | Hyp . 2 Concl . CON . 1 P. 11 . 2 P. 3. Pst . 1 . DEM . 1 C. 2 . 2 Add . 3 Ax . 2 . 4 C. 1 . 5 P. 47 . 6 Hyp . 7 ...
Términos y frases comunes
12 Recap 9 Ax 9 Concl 9 Recap adjacent Algebra and Arithmetic alternate angles equal angle contained angle triangle apply BOOKS OF EUCLID Construction and Demonstration consult the Gradations Data describe a parallelogram DIAGRAMS equal and parallel equal angles equal bases equal sides Equal triangles EUCLID BOOKS EXERCISES EXPLANATORY PREFACE Exposition four rt GEOMETRICAL REASONING GEOMETRY given in numbers given point given rectilineal angle given st given triangle GRADATIONS IN EUCLID greater angle hypotenuse Learner Let the equal line falling margin opposite parallel st parallels are equal PEN-AND-INK EXAMINATIONS perp PRICE Principles printed PROB PROP Quæs recapitulatory rectil rectilineal figure references SCHOL SECOND BOOKS segments Series side equal side together equal SKELETON PROPOSITIONS squares be given squares described step by step THEOR third angle Triangles upon equal truths uniformity vertex vertical written دو وو
Pasajes populares
Página xxiv - If two triangles have two sides of the one equal to two sides of the other, each to each, but the base of the one greater than the base of the other; the angle also contained by the sides of that which has the greater base, shall be greater than the angle contained by the sides equal to them of the other.
Página xx - Therefore any two sides, &c. QED PROP. XXI. THEOR. If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.
Página xxiv - IF two triangles have two angles of one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal angles, or...
Página xli - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página xliii - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC...
Página xxxviii - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Página xxi - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third (20.
Página xl - If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle.
Página xxxviii - Triangles upon equal bases, and between the same parallels, are equal to one another.