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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...
Volledige weergave - 1775
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...
Volledige weergave - 1762
AC is equal alſo angle ABC angle BAC baſe BC BC is given becauſe the angle Book caſe cauſe circle ABCD circumference cone conſequently conſtrućtion cylinder demonſtrated deſcribed drawn equal angles equiangular equimultiples exceſs figure firſt fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join laſt leſs likewiſe muſt oppoſite P R O parallel parallelepipeds parallelogram paſs thro perpendicular plane angles priſms Prop proportionals Propoſition pyramid reŽtangle right angles ſaid ſame manner ſame multiple ſame ratio ſame reaſon ſecond ſegment ſhall ſhewn ſides ſides BA ſimilar ſince ſolid angle ſome ſļuare ſpace ſphere ſquare of AC ſtraight line AB ſtraight line BC ſum T H E O theſe thoſe triangle ABC uſe wherefore
Pagina 156 - 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.
Pagina 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Pagina 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.
Pagina 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Pagina 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Pagina 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Pagina 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.
Pagina 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.