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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Side 3
... equal to the given line as being radii of the same circle , and they are .. each other ( per ax . 1. ) to Note . - No more than two equilateral triangles can be formed on the same right line , viz . one on each side of it . Those ...
... equal to the given line as being radii of the same circle , and they are .. each other ( per ax . 1. ) to Note . - No more than two equilateral triangles can be formed on the same right line , viz . one on each side of it . Those ...
Side 4
... equal to two sides of the other , and the angle contained by those two sides of the one equal to the angle contained by the two sides equal to them of the other , their bases or third sides shall be equal , also the angles at the bases ...
... equal to two sides of the other , and the angle contained by those two sides of the one equal to the angle contained by the two sides equal to them of the other , their bases or third sides shall be equal , also the angles at the bases ...
Side 5
... equal to one another ; and if the equal sides be produced the angles below the base shall be also equal . Assume points on the legs below the base equidistant from the vertex ; and from these assumed points draw transverse lines to the ...
... equal to one another ; and if the equal sides be produced the angles below the base shall be also equal . Assume points on the legs below the base equidistant from the vertex ; and from these assumed points draw transverse lines to the ...
Side 6
... equal . PROP . 8 , THEOR , If two triangles have two sides of the one respectively , equal to two sides of the other , and also have the base of the one equal to the base of the other , the angles contained by the equal sides are also ...
... equal . PROP . 8 , THEOR , If two triangles have two sides of the one respectively , equal to two sides of the other , and also have the base of the one equal to the base of the other , the angles contained by the equal sides are also ...
Side 9
... equal to two right angles , those two right lines form one continued right line . For let it be supposed that one of them be produced beyond the vertex of the angles so as that the produced part shall not coincide with the other : then ...
... equal to two right angles , those two right lines form one continued right line . For let it be supposed that one of them be produced beyond the vertex of the angles so as that the produced part shall not coincide with the other : then ...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... Euclides Uten tilgangsbegrensning - 1833 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 128 - The angle at the centre of a circle is double the angle at the circumference on the same arc.
Side 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.
Side 111 - In any triangle, the square of the side subtending an acute angle is less than the sum of the squares of the...
Side 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.
Side 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.
Side 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.
Side 20 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 116 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Side 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.
Side 28 - Similar triangles are to one another in the duplicate ratio of their homologous sides.