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 65.
Σελίδα 8
... proved as the former ( per 8th ) PROP . 13 , THEOR . When a right line standing upon another makes angles with it , they are either two right angles or are together equal to two right angles , If the right line standing on the other be ...
... proved as the former ( per 8th ) PROP . 13 , THEOR . When a right line standing upon another makes angles with it , they are either two right angles or are together equal to two right angles , If the right line standing on the other be ...
Σελίδα 9
... opposite and the sides containing them by con struction ) But the external angle is greater than the former angle and .. greater than the latter . This exter- nal angle is proved greater than the other internal remote 9.
... opposite and the sides containing them by con struction ) But the external angle is greater than the former angle and .. greater than the latter . This exter- nal angle is proved greater than the other internal remote 9.
Σελίδα 10
Euclides James Luby. nal angle is proved greater than the other internal remote angle by producing the opposite side beyond the vertex of this external angle , and proving as before the new external angle , thus formed greater than that ...
Euclides James Luby. nal angle is proved greater than the other internal remote angle by producing the opposite side beyond the vertex of this external angle , and proving as before the new external angle , thus formed greater than that ...
Σελίδα 12
... proved in the same way that the two drawn lines are less than the produced line and added seg ... a fortiori & c . Secondly , the angle con- tained by those drawn lines is external to an angle that is external to the angle contained by ...
... proved in the same way that the two drawn lines are less than the produced line and added seg ... a fortiori & c . Secondly , the angle con- tained by those drawn lines is external to an angle that is external to the angle contained by ...
Σελίδα 14
... proved , that the sides between the angles are , for if they were not . an 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 ...
... proved , that the sides between the angles are , for if they were not . an 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 ...
Άλλες εκδόσεις - Προβολή όλων
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.