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 CorrectedDesilver, 1829 - 516 sider |
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Side 16
... equilateral triangle is also equi- angular . PROP . VI . THEOR . Ir two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal an- gles , shall be equal to one another . Let ABC be a ...
... equilateral triangle is also equi- angular . PROP . VI . THEOR . Ir two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal an- gles , shall be equal to one another . Let ABC be a ...
Side 17
... equiangular triangle is also equilateral . PROP . VII . THEOR . C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one an ...
... equiangular triangle is also equilateral . PROP . VII . THEOR . C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one an ...
Side 101
... PROB . In a given circle to inscribe a triangle equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle ; it is required to inscribe in the circle ABC a BOOK IV . 101 THE ELEMENTS OF EUCLID .
... PROB . In a given circle to inscribe a triangle equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle ; it is required to inscribe in the circle ABC a BOOK IV . 101 THE ELEMENTS OF EUCLID .
Side 102
... equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle ; it is required to describe a triangle about the circle ABC equi- angular to the triangle DEF . Produce EF both ways to the points G , H , and ...
... equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle ; it is required to describe a triangle about the circle ABC equi- angular to the triangle DEF . Produce EF both ways to the points G , H , and ...
Side 103
... equiangular to the triangle DEF : and it is described about the circle ABC . Which was to be done . PROP . IV . PROB . To inscribe a circle in a given triangle . * Let the given triangle be ABC ; it is required to inscribe a circle in ...
... equiangular to the triangle DEF : and it is described about the circle ABC . Which was to be done . PROP . IV . PROB . To inscribe a circle in a given triangle . * Let the given triangle be ABC ; it is required to inscribe a circle in ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine 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 multiple 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 sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 81 - The angles in the same segment of a circle are equal to one another.
Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.
Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Side 24 - Any two sides of a triangle are together greater than the third side.