Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ... |
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Seite 104
Ratio is a mutual relation of two magnitudes of the same ' kind to one another , in respect of quantity . ' IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other .
Ratio is a mutual relation of two magnitudes of the same ' kind to one another , in respect of quantity . ' IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other .
Seite 105
Magnitudes which have the same ratio are called propor- tionals . ' N.B. When four magnitudes are propor- ' tionals , it is usually expressed by saying , the first is ' to the second , as the third to the fourth . ' VII .
Magnitudes which have the same ratio are called propor- tionals . ' N.B. When four magnitudes are propor- ' tionals , it is usually expressed by saying , the first is ' to the second , as the third to the fourth . ' VII .
Seite 105
ratio of B to C , and the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B to C the same ratio that G has to H ...
ratio of B to C , and the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B to C the same ratio that G has to H ...
Seite 105
... and as the third is to the fourth of the first rank , so is the third from the last to the last but a 4 Prop . lib . 2 , Archimedis de sphærâ et cylindro . ratio of B to C , and the ratio of BOOK V. DEFINITIONS . 107.
... and as the third is to the fourth of the first rank , so is the third from the last to the last but a 4 Prop . lib . 2 , Archimedis de sphærâ et cylindro . ratio of B to C , and the ratio of BOOK V. DEFINITIONS . 107.
Seite 106
ratio of B to C , and the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B to C the same ratio that G has to H ...
ratio of B to C , and the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B to C the same ratio that G has to H ...
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ABCD angle ABC angle ACB angle BAC base base BC BC is equal bisected centre circle circle ABC circumference common compounded Constr contained demonstrated describe diameter divided double draw drawn equal angles equal to F equiangular equilateral equimultiples extremity fall fore four fourth given straight line greater join less Let ABC likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular plane produced proportionals Q. E. D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar square square of AC straight line AC Take taken THEOR THEOR.-If third touches the circle triangle ABC wherefore whole
Beliebte Passagen
Seite 12 - If two triangles have two sides of the one equal to two sides of the...
Seite 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Seite 143 - 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 69 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Seite 20 - 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. Let the two straight lines BD.
Seite 102 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times
Seite 44 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Seite 71 - The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles.
Seite 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Seite 83 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Bibliografische Informationen
| Titel | Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ... Cambr. ed |
| Autor/in | Euclid |
| Herausgeber | Robert Simson |
| Übersetzt von | Robert Simson |
| Verlag | T. Stevenson, 1845 |
| Original von | Oxford University |
| Digitalisiert | 4. Okt. 2006 |
| Länge | 199 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |