The Elements of Geometry, Symbolically Arranged |
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Página 17
... manner of doing which has not been previously explained . The equality of the s on the oppo . side of the base will follow from Prop . 12 . PROP . VI . THEOR . 6. 1 Eu . If two angles of a triangle be equal to one another , the sides ...
... manner of doing which has not been previously explained . The equality of the s on the oppo . side of the base will follow from Prop . 12 . PROP . VI . THEOR . 6. 1 Eu . If two angles of a triangle be equal to one another , the sides ...
Página 24
... manner it may be shown , that no other line but BD can be in the same str . line with BC . Wherefore , if at a point , & c . PROP . XIV . THEOR . 15. 1 Eu . If two straight lines cut one another , the ver- tical or opposite angles shall ...
... manner it may be shown , that no other line but BD can be in the same str . line with BC . Wherefore , if at a point , & c . PROP . XIV . THEOR . 15. 1 Eu . If two straight lines cut one another , the ver- tical or opposite angles shall ...
Página 25
... manner it may be shown , that Z CEB - AED . Therefore , if two straight lines , & c . COR . 1. - If two str . lines cut one another , thes which they make at the pt . where they cut , are together equal to 4 rt . s . COR . 2. - All the ...
... manner it may be shown , that Z CEB - AED . Therefore , if two straight lines , & c . COR . 1. - If two str . lines cut one another , thes which they make at the pt . where they cut , are together equal to 4 rt . s . COR . 2. - All the ...
Página 26
... Produce BC to D. ACD > < ABC , the int . and add ACB to each , :: 2 ACD + ACB > < ABC + ACB ; Prop . 12. but ACD +2 ACB = 2 rt . s , :: Z ABC + △ ACB < 2 rt . s . In like manner it may be proved , that BAC 26 GEOMETRY .
... Produce BC to D. ACD > < ABC , the int . and add ACB to each , :: 2 ACD + ACB > < ABC + ACB ; Prop . 12. but ACD +2 ACB = 2 rt . s , :: Z ABC + △ ACB < 2 rt . s . In like manner it may be proved , that BAC 26 GEOMETRY .
Página 27
... 19. 1Eu . The greater angle of every triangle is sub- tended by the greater side ; or has the greater side opposite to it . Prop . 5 . By Hyp . Prop . 17 C 2 PROP . XVII . XVIII . 27 In like manner it may be proved, that ...
... 19. 1Eu . The greater angle of every triangle is sub- tended by the greater side ; or has the greater side opposite to it . Prop . 5 . By Hyp . Prop . 17 C 2 PROP . XVII . XVIII . 27 In like manner it may be proved, that ...
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The Elements of Geometry, Symbolically Arranged Great Britain Admiralty Sin vista previa disponible - 2016 |
Términos y frases comunes
2ndly ABCD AC² angle contained angle equal base BC CB² centre circle circumference coincides Constr descr diam diameter dist divided equal angles equiangular equilat exterior angle figure given point given str given straight line gnomon greater isosceles triangle join Let ABC Let str Let the str line be drawn meet number of equal oppo opposite angle opposite sides parallel parallelogram perpendicular polygon PROB prod Prop rect rectangle contained rectilineal right angles right-angled triangle semi sides equal square THEOR touch trapezium Wherefore whole fig Нур
Pasajes populares
Página 60 - 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.
Página 34 - 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...
Página 62 - 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...
Página 38 - 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...
Página 63 - 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.
Página 23 - 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.
Página 39 - 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...
Página 5 - 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.
Página 79 - 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.
Página 21 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.