The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |
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Page 9
... drawn from a certain point within the figure to the circumference , are equal to one another : XVI . And this point is called the centre of the circle . XVII . A diameter of a circle is a straight line drawn through the cen- tre , and ...
... drawn from a certain point within the figure to the circumference , are equal to one another : XVI . And this point is called the centre of the circle . XVII . A diameter of a circle is a straight line drawn through the cen- tre , and ...
Page 20
... drawn from the given point C is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; the two sides DC , CF , A D are equal to the two EC , CF , each to each ; and the ...
... drawn from the given point C is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; the two sides DC , CF , A D are equal to the two EC , CF , each to each ; and the ...
Page 21
... drawn from the given point C , is perpendicular to the given straight line AB . Because FH is equal to HG , and HC common to the two tri- angles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the ...
... drawn from the given point C , is perpendicular to the given straight line AB . Because FH is equal to HG , and HC common to the two tri- angles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the ...
Page 26
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . * Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
... drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle , but shall contain a greater angle . * Let the two straight lines BD , CD be drawn from B , C , the ends of the side ...
Page 35
... drawn through the given point A parallel to the given straight line BC . Which was to be done . PROP . XXXII . THEOR . Ir a side of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the ...
... drawn through the given point A parallel to the given straight line BC . Which was to be done . PROP . XXXII . THEOR . Ir a side of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore