The Element of GeometryW.E. Dean, 1836 - 114 Seiten |
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Seite 63
... ratio . II . Each of the quantities in a ratio may be called a term . III . If the ratio of the first to the second is the same with that of the third to the fourth , the quantities may be said to be in geometrical pro- portion . IV ...
... ratio . II . Each of the quantities in a ratio may be called a term . III . If the ratio of the first to the second is the same with that of the third to the fourth , the quantities may be said to be in geometrical pro- portion . IV ...
Seite 64
... ratio of the first to the third is compounded of the ra- tio of the first to the second , and of the second to the third . And when the ratio of the second to the third , is the same with that of the first to the second , the ratio of ...
... ratio of the first to the third is compounded of the ra- tio of the first to the second , and of the second to the third . And when the ratio of the second to the third , is the same with that of the first to the second , the ratio of ...
Seite 66
... ratio to the same ; and the same has the same ratio to equal quantities . Let A and B be equal quantities , and C any other quantity ; as A : C : B : C. Because A is equal to B , C is the same part of A that it is of B , A B and ...
... ratio to the same ; and the same has the same ratio to equal quantities . Let A and B be equal quantities , and C any other quantity ; as A : C : B : C. Because A is equal to B , C is the same part of A that it is of B , A B and ...
Seite 67
... Ratios that are the same to the same ratio , are the same to one another . Let A B C D , and C : D :: E : F : : Because A : B :: C : D , A : B :: E : F. A B D C ( Def . 20. 4. ) ; and because C : D :: E : F , CE D F A E ; and therefore ...
... Ratios that are the same to the same ratio , are the same to one another . Let A B C D , and C : D :: E : F : : Because A : B :: C : D , A : B :: E : F. A B D C ( Def . 20. 4. ) ; and because C : D :: E : F , CE D F A E ; and therefore ...
Seite 68
... ratio ; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last . This is usually cited by the words " ex æquali in proportione pertur- bata , " or " ex æquo perturbato ...
... ratio ; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last . This is usually cited by the words " ex æquali in proportione pertur- bata , " or " ex æquo perturbato ...
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The Element of Geometry (Classic Reprint) Formerly Chairman Department of Immunology John Playfair,John Playfair Keine Leseprobe verfügbar - 2017 |
Häufige Begriffe und Wortgruppen
AB is equal AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF arc AC base BC bisect called centre circle ABCD circle EFGH coincide described divided drawn duplicate ratio equal 17 equal angles equal circles equal to CD equiangular FGHKL fore four right angles given straight line gnomon greater homologous sides join less Let ABC Let the straight opposite angles parallel parallelogram perpendicular polygon PROB produced Q. E. D. PROP radius rectangle BC rectangle contained rectilineal figure remaining angle right angled triangle secant segment side AC similar sine square of AC straight line AB straight line AC THEOR touches the circle triangle ABC twice the rectangle wherefore whole angle
Beliebte Passagen
Seite 25 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Seite 13 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line E iR.
Seite 4 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Seite 29 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Seite 90 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Seite 87 - ... magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Seite 1 - If two triangles have two sides of the one equal to two sides of the...
Seite 13 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Seite 64 - 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 19 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Bibliografische Informationen
| Titel | The Element of Geometry |
| Autor/in | John Playfair |
| Verlag | W.E. Dean, 1836 |
| Original von | New York Public Library |
| Digitalisiert | 21. Juni 2006 |
| Länge | 114 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |