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 42.
Σελίδα 47
... inscribe a square in an equilateral triangle ( ABG ) . Fig . 36 . ANALYSIS . Suppose CF to be the required , let fall a perpen- dicular BD , join BE . Then LF is to FB , ( since the triangle LBF is evidently equilateral , ) . FB is to ...
... inscribe a square in an equilateral triangle ( ABG ) . Fig . 36 . ANALYSIS . Suppose CF to be the required , let fall a perpen- dicular BD , join BE . Then LF is to FB , ( since the triangle LBF is evidently equilateral , ) . FB is to ...
Σελίδα 74
... inscribed in a triangle , ( ABC , ) is half the altitude of the tri- angle , its base shall be equal to half the base of the triangle . Fig . 64 , For , draw AI at right angles to the base BC . Then , because AI is bisected in U , and ...
... inscribed in a triangle , ( ABC , ) is half the altitude of the tri- angle , its base shall be equal to half the base of the triangle . Fig . 64 , For , draw AI at right angles to the base BC . Then , because AI is bisected in U , and ...
Σελίδα 75
... inscribed in a tri- angle , ( ABC , ) the greatest is that ( LK ) whose sides are respectively equal to the semi - base and semi - altitude of the triangle . Fig . 64 For , let DG be any other parallelogram , it is less than LK . Draw ...
... inscribed in a tri- angle , ( ABC , ) the greatest is that ( LK ) whose sides are respectively equal to the semi - base and semi - altitude of the triangle . Fig . 64 For , let DG be any other parallelogram , it is less than LK . Draw ...
Σελίδα 81
... inscribe in a given square ( DCG ) a right line parallel to a right line ( LG ) given in position and equal to [ FI ] given in magnitude , not greater than the diameter of the square . Fig . 11 . Draw from any angle BDE of the given DK ...
... inscribe in a given square ( DCG ) a right line parallel to a right line ( LG ) given in position and equal to [ FI ] given in magnitude , not greater than the diameter of the square . Fig . 11 . Draw from any angle BDE of the given DK ...
Σελίδα 87
... is less than FGE . = PROP . 136 , PROB . In a given square [ DC ] to inscribe an equilateral tri ingle , one of whose angular points shall be in an an angular point [ B ] of the given square . Fig . 11 . Draw a diagonal BE ; at 87.
... is less than FGE . = PROP . 136 , PROB . In a given square [ DC ] to inscribe an equilateral tri ingle , one of whose angular points shall be in an an angular point [ B ] of the given square . Fig . 11 . Draw a diagonal BE ; at 87.
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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.