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 3
... line as radius describe two circles , ( per post . 3. ) ; from a point in which those circles intersect one another draw lines to the extremities of the given one ; those three lines form an equilateral triangle . For each of the drawn ...
... line as radius describe two circles , ( per post . 3. ) ; from a point in which those circles intersect one another draw lines to the extremities of the given one ; those three lines form an equilateral triangle . For each of the drawn ...
Page 4
... drawn . For it is to the produced part of the other leg ; since the whole produced legs are = , and the parts of ... lines a part equal to the less . = From either extremity of the greater draw a line = to the less ( per Prop . 2 , ) and with ...
... drawn . For it is to the produced part of the other leg ; since the whole produced legs are = , and the parts of ... lines a part equal to the less . = From either extremity of the greater draw a line = to the less ( per Prop . 2 , ) and with ...
Page 8
... drawn to the point of bisection is per- pendicular to the given line . This can be proved as the former ( per 8th ) ... lines stand on the same right line at the same point , they make angles , which taken to- gether are equal to two right ...
... drawn to the point of bisection is per- pendicular to the given line . This can be proved as the former ( per 8th ) ... lines stand on the same right line at the same point , they make angles , which taken to- gether are equal to two right ...
Page 11
... drawn to the same right line , of which one is perpendicular to it , and the other not , the perpendicular is the ... lines drawn to any point within a triangle from the extremities of any side , are together less than the sum of the ...
... drawn to the same right line , of which one is perpendicular to it , and the other not , the perpendicular is the ... lines drawn to any point within a triangle from the extremities of any side , are together less than the sum of the ...
Page 12
... 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 the two sides of ' original triangle ...
... 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 the two sides of ' original triangle ...
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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.