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 100.
Σελίδα 11
... half of bisected angle , as being external to it . ) Hence it is evident that the difference between two sides of a triangle is less than the third side . PROP . 21 , THEOR . Two right lines drawn to any point within a triangle from the ...
... half of bisected angle , as being external to it . ) Hence it is evident that the difference between two sides of a triangle is less than the third side . PROP . 21 , THEOR . Two right lines drawn to any point within a triangle from the ...
Σελίδα 17
... half a right angle . Cor . 4. Each angle of an equilateral triangle is to a third part of two right angles . Cor . 5 Hence can be derived a method of trisecting a right angle ; by assuming any portion on one of the legs from the vertex ...
... half a right angle . Cor . 4. Each angle of an equilateral triangle is to a third part of two right angles . Cor . 5 Hence can be derived a method of trisecting a right angle ; by assuming any portion on one of the legs from the vertex ...
Σελίδα 21
... half the pa- rallelogram , .. the parallelogram is to the whole triangle . PROP . 42 , PROB . To construct a parallelogram equal to a given triangle , and having an angle equal to a given one . Through the vertex of the triangle draw a ...
... half the pa- rallelogram , .. the parallelogram is to the whole triangle . PROP . 42 , PROB . To construct a parallelogram equal to a given triangle , and having an angle equal to a given one . Through the vertex of the triangle draw a ...
Σελίδα 22
... half of a right angle , .. the adjacent sides are and also the opposite sides .. the figures are equilat . to each other , and also rectangular . PROP . 44 , THEOR . To a given right line , to apply a parallelogram equal to a given ...
... half of a right angle , .. the adjacent sides are and also the opposite sides .. the figures are equilat . to each other , and also rectangular . PROP . 44 , THEOR . To a given right line , to apply a parallelogram equal to a given ...
Σελίδα 23
... half of one ' . can be proved to a triangle which is half of the other ( prop . 4. ) .. the squares them- selves which are the doubles of those triangles are = Cor . 2. If two squares be equal , their sides are equal . For if not cut ...
... half of one ' . can be proved to a triangle which is half of the other ( prop . 4. ) .. the squares them- selves which are the doubles of those triangles are = Cor . 2. If two squares be equal , their sides are equal . For if not cut ...
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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.