The Elements of Geometry, Symbolically Arranged |
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Seite 89
And in any proportion if the means are equal to each other , i . e . if a : b :: b : c , thén b is said to be a mean proportional between a and b . DEF . 3. - Similar rectilineal figures are those which have their respective angles ...
And in any proportion if the means are equal to each other , i . e . if a : b :: b : c , thén b is said to be a mean proportional between a and b . DEF . 3. - Similar rectilineal figures are those which have their respective angles ...
Seite 91
If there be any number of proportional quantities , represented numerically as a : b :: c : d :: e : f , & c .; then will one antecedent be to its consequent , as the sum of all the antece- dents to the sum of all the consequents ; or a ...
If there be any number of proportional quantities , represented numerically as a : b :: c : d :: e : f , & c .; then will one antecedent be to its consequent , as the sum of all the antece- dents to the sum of all the consequents ; or a ...
Seite 93
If a straight line be drawn parallel to one of the sides of a triangle , it shall cut the other sides proportionally and if the sides be cut proportionally , the straight line which joins the points of section shall be parallel to the ...
If a straight line be drawn parallel to one of the sides of a triangle , it shall cut the other sides proportionally and if the sides be cut proportionally , the straight line which joins the points of section shall be parallel to the ...
Seite 94
Let the sides AB , AC of the ABC , be cut proportionally in pts . D , E , so that DB : AD : : EC : AE , or AB : AC :: AD : AE ; join DE : then shall DE || BC . ABDE ᎠᏴ = ΔADE AD 9 As before ACDE EC = ΔADE AE ᎠᏴ EC Hyp . and since AD ...
Let the sides AB , AC of the ABC , be cut proportionally in pts . D , E , so that DB : AD : : EC : AE , or AB : AC :: AD : AE ; join DE : then shall DE || BC . ABDE ᎠᏴ = ΔADE AD 9 As before ACDE EC = ΔADE AE ᎠᏴ EC Hyp . and since AD ...
Seite 98
The perpendicular AD is a mean proportional between the segments BD , DC , of the base BC . And each of the sides AB , AC , is a mean proportional between the base BC and the segment adjacent to the side .
The perpendicular AD is a mean proportional between the segments BD , DC , of the base BC . And each of the sides AB , AC , is a mean proportional between the base BC and the segment adjacent to the side .
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The Elements of Geometry, Symbolically Arranged Great Britain Admiralty Keine Leseprobe verfügbar - 2016 |
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ABCD AC² angle contained base base BC bisect called centre circle circumference coincides common Constr descr described diam diameter dist divided draw equal equal angles equiangular equilat expressed extremities falls figure given point given straight line gnomon greater half isosceles join less Let ABC line drawn manner mean meet oppo opposite angle opposite sides parallel parallelogram pass perpendicular plane polygon PROB prod produced Prop proportional proposition proved quantities ratio rect rectangle contained rectilineal remain right angles segments shown sides square THEOR touch triangle unequal Wherefore Нур
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Seite 58 - 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 of the line between the points of section, is equal to the square of half the line.
Seite 32 - If two triangles have two angles of the 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...
Seite 60 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Seite 36 - Wherefore, if a straight line, &c. QB D. PROPOSITION XXVIII. THEOB.—-If a straight line, falling upon two other straight lines, make the exterior angle equal to...
Seite 61 - 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 in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Seite 21 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Seite 37 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Seite 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.
Seite 77 - 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 19 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Bibliografische Informationen
| Titel | The Elements of Geometry, Symbolically Arranged |
| Autor/in | Great Britain. Admiralty |
| Ausgabe | 2 |
| Veröffentlicht | 1846 |
| Original von | Oxford University |
| Digitalisiert | 10. Okt. 2006 |
| Zitat exportieren | BiBTeX EndNote RefMan |