The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
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Side 7
... Q. E. F. The construction of this problem might be improved thus : - Join AB . Upon A B describe the equilateral triangle ABD . From the centre B , at the distance BC , describe the circle CG H. Produce DB to BOOK I. PROP . II .
... Q. E. F. The construction of this problem might be improved thus : - Join AB . Upon A B describe the equilateral triangle ABD . From the centre B , at the distance BC , describe the circle CG H. Produce DB to BOOK I. PROP . II .
Side 10
... join DC . Because in the two triangles DBC , ACB , the side DB is equal to the side AC , and BC is common to both , the two sides , DB , BC are equal to the two sides AC , CB , each to each . And the angle DBC is equal to the angle ...
... join DC . Because in the two triangles DBC , ACB , the side DB is equal to the side AC , and BC is common to both , the two sides , DB , BC are equal to the two sides AC , CB , each to each . And the angle DBC is equal to the angle ...
Side 11
... Join CD . First , let the vertex of each triangle be without the other triangle . Because AC is equal ( Hyp . ) to AD in the triangle ACD , the angle ACD is equal ( I. 5 ) to the angle ADC . But the angle ACD is greater ( Ax . 9 ) than ...
... Join CD . First , let the vertex of each triangle be without the other triangle . Because AC is equal ( Hyp . ) to AD in the triangle ACD , the angle ACD is equal ( I. 5 ) to the angle ADC . But the angle ACD is greater ( Ax . 9 ) than ...
Side 12
... Join DE . Upon DE , opposite to the triangle DAE , describe ( I. 1 ) an equilateral triangle DEF . Join AF . The straight line AF bisects the angle BAC . Because AD is equal ( Const . ) to AE , and AF is common to the two triangles DAF ...
... Join DE . Upon DE , opposite to the triangle DAE , describe ( I. 1 ) an equilateral triangle DEF . Join AF . The straight line AF bisects the angle BAC . Because AD is equal ( Const . ) to AE , and AF is common to the two triangles DAF ...
Side 13
... join FC . The straight line FC drawn from the given point C , is at right angles to the given straight line AB . A D F EB Because DC is equal ( Const . ) to CE , and FC common to the two triangles DCF , ECF , the two sides D C , CF ...
... join FC . The straight line FC drawn from the given point C , is at right angles to the given straight line AB . A D F EB Because DC is equal ( Const . ) to CE , and FC common to the two triangles DCF , ECF , the two sides D C , CF ...
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The Elements of geometry; or, The first six books, with the eleventh and ... Euclides Uten tilgangsbegrensning - 1881 |
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
A B C ABC is equal ABCD altitude angle ABC angle BAC base bisected Book centre circle circle ABC circumference common compounded cone Const contained Corollary cylinder definition demonstration described diameter divided double draw drawn equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half homologous inscribed join less magnitudes manner meet multiple opposite parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proposition proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar similarly solid solid angle sphere square Take taken THEOREM third touch triangle ABC vertex Wherefore whole
Populære avsnitt
Side 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 42 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 130 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 143 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Side 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Side 115 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Side 45 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...