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 33.
Σελίδα 9
... external angle is greater than either of the internal opposite angles . For connect with the opposite angle the middle point , of the side conterminous with the produced part and pro- duce this connecting line till the produced part is ...
... external angle is greater than either of the internal opposite angles . For connect with the opposite angle the middle point , of the side conterminous with the produced part and pro- duce this connecting line till the produced part is ...
Σελίδα 10
... external angle , and proving as before the new external angle , thus formed greater than that internal angle : but this external angle is to the given one , ( by the 15th . ) Cor . 1. If from any point two right lines be drawn to the ...
... external angle , and proving as before the new external angle , thus formed greater than that internal angle : but this external angle is to the given one , ( by the 15th . ) Cor . 1. If from any point two right lines be drawn to the ...
Σελίδα 11
... external to it by the 16th . ) the entire angle opposite the greater side is much greater than the angle opposite the less . PROP . 19 , THEOR . If in any triangle one angle be greater than an other , the side which is opposite the ...
... external to it by the 16th . ) the entire angle opposite the greater side is much greater than the angle opposite the less . PROP . 19 , THEOR . If in any triangle one angle be greater than an other , the side which is opposite the ...
Σελίδα 12
... external to an angle that is external to the angle contained by the two sides of ' original triangle and ... much greater than it . PROP . 22 , PROB . Given three right lines of which any two together are greater than the third to ...
... external to an angle that is external to the angle contained by the two sides of ' original triangle and ... much greater than it . PROP . 22 , PROB . Given three right lines of which any two together are greater than the third to ...
Σελίδα 14
... external angle of a triangle would be = to an internal remote . Schol . It is evident that the triangles themselves are equal . Cor , 1. In an isosceles triangle , the right line drawn from the vertex perpendicular to the base , bisects ...
... external angle of a triangle would be = to an internal remote . Schol . It is evident that the triangles themselves are equal . Cor , 1. In an isosceles triangle , the right line drawn from the vertex perpendicular to the base , bisects ...
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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.