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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Page 4
... opposite the equal sides , and the whole triangles shall be equal . If the two triangles be so applied to one another , that the vertex of one may coincide with that of the other , and a side of one coincide with a side equal to it of ...
... opposite the equal sides , and the whole triangles shall be equal . If the two triangles be so applied to one another , that the vertex of one may coincide with that of the other , and a side of one coincide with a side equal to it of ...
Page 5
... side of isosceles triangle and cut off seg . in one , respectively = to a ... opposite the base are = ( per demon . ) and the sides containing them are ... opposite to them are also equal , For if they be not let one of them be greater ...
... side of isosceles triangle and cut off seg . in one , respectively = to a ... opposite the base are = ( per demon . ) and the sides containing them are ... opposite to them are also equal , For if they be not let one of them be greater ...
Page 6
... sides are equal . If it be possible that there can , 1st , let the vertex of one fall without the other , draw a right connecting their ver- tices ... side of the other , it is evident that two of the con- terminous sides are ... opposite 6.
... sides are equal . If it be possible that there can , 1st , let the vertex of one fall without the other , draw a right connecting their ver- tices ... side of the other , it is evident that two of the con- terminous sides are ... opposite 6.
Page 7
... side of the connecting line remote from the given angle , describe an equilateral triangle , the right line joining ... opposite the given line , the line bisecting this angle , ( if produced to it , ) will bisect the given right line . For ...
... side of the connecting line remote from the given angle , describe an equilateral triangle , the right line joining ... opposite the given line , the line bisecting this angle , ( if produced to it , ) will bisect the given right line . For ...
Page 9
... opposite sides , make angles with it , which are together equal to two right angles , those two right lines form one ... side of a triangle be produced the external angle is greater than either of the internal opposite angles . For ...
... opposite sides , make angles with it , which are together equal to two right angles , those two right lines form one ... side of a triangle be produced the external angle is greater than either of the internal opposite angles . For ...
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Common terms and phrases
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
Popular passages
Page 128 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Page 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.
Page 111 - In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the...
Page 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.
Page 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.
Page 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.
Page 20 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Page 116 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Page 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.
Page 28 - Similar triangles are to one another in the duplicate ratio of their homologous sides.