The Elements of geometry [Euclid book 1-3] in general terms, with notes &c. &c. Also a variety of problems & theorems. [Ed. by J. Luby. With] The elements of plane geometry, comprising the definitions of the fifth book, and the sixth book in general terms, with notes [&c.] by J. Luby [described as] Pt. 31821 |
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Αποτελέσματα 1 - 5 από τα 24.
Σελίδα 8
... standing upon another makes angles with it , they are either two right angles or are together equal to two right angles ... stand on the same right line at the same point , they make angles , which taken to- gether are equal to two right ...
... standing upon another makes angles with it , they are either two right angles or are together equal to two right angles ... stand on the same right line at the same point , they make angles , which taken to- gether are equal to two right ...
Σελίδα 29
... standing on the same base must be between the same parallels ( 39. 1. Elr . ) Therefore , it is evident , that if you bisect DF in C join AE and draw CB parallel to it , that the straight line drawn from the given point - A to B ...
... standing on the same base must be between the same parallels ( 39. 1. Elr . ) Therefore , it is evident , that if you bisect DF in C join AE and draw CB parallel to it , that the straight line drawn from the given point - A to B ...
Σελίδα 31
... stand on equal bases . Fig . 6 . For , if they do not , cut from the greater BC a part GC to EF , connect GA . Then the triangles GAC , EDF are ( 38. 1. Elr . ) .. GAC is to ABC , a part to the whole which is absurd . PROP . 6 , THEOR ...
... stand on equal bases . Fig . 6 . For , if they do not , cut from the greater BC a part GC to EF , connect GA . Then the triangles GAC , EDF are ( 38. 1. Elr . ) .. GAC is to ABC , a part to the whole which is absurd . PROP . 6 , THEOR ...
Σελίδα 133
... stand . Then , because the angle thus formed , stand on the same arch with the given angle at the circumference , it is to it and .. to the other given angle ( to which it is external or internal ) contrary to prop . 18 , b . 1 . PROP ...
... stand . Then , because the angle thus formed , stand on the same arch with the given angle at the circumference , it is to it and .. to the other given angle ( to which it is external or internal ) contrary to prop . 18 , b . 1 . PROP ...
Σελίδα 134
... stand , and draw from the point in which either of those connecting lines cuts the inner seg . a right line to the opposite extremity . Then since the segments are similar , the angles they contain are , ( def . 10 , b . 3 , ) but one ...
... stand , and draw from the point in which either of those connecting lines cuts the inner seg . a right line to the opposite extremity . Then since the segments are similar , the angles they contain are , ( def . 10 , b . 3 , ) but one ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent ANALYSIS angle ABC angle contained arches bisecting line chord circumference connecting line conterminous dedu describe a circle diagonal diameter directum divided draw a right drawn line equiangular equilateral triangle evident external angle extremity given angle given circle given in position given line given point given ratio given right line given side gonal half the given hypothenuse inscribed intercept intersect isosceles triangle less lesser let fall line bisecting lines be drawn magnitude mean proportional meet middle point opposite angle opposite side parallelogram pass pendicular perpen perpendicular point of bisection point of contact point of section polygons PORISMS PROB PROP radii radius rect rectangle required triangle right angled triangle right line drawn segts semicircle semiperimeter side subtending square Suppose tangent THEOR triangle ABC vertex vertical angle whole line
Δημοφιλή αποσπάσματα
Σελίδα 128 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Σελίδα 26 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean ; and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Σελίδα 111 - In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the...
Σελίδα 4 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.
Σελίδα 98 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 2 - Convertendo ; when it is .concluded, that if there be four magnitudes proportional, the first is to the sum or difference of the first and second, as the third is to the sum or difference of the third and fourth.
Σελίδα 20 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Σελίδα 116 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Σελίδα 156 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Σελίδα 28 - Similar triangles are to one another in the duplicate ratio of their homologous sides.