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The First Two Books of the Elements of Euclid ... with Additional Figures ...
Uten tilgangsbegrensning - 1852
ABCD added Ancient angle ABC angle ACB angle BAC angles equal Arithmetic base BC BC is equal bisected BOOK bound centre circle cloth coincide College common construct corrected demonstrated describe diameter difference distance divided double draw drawn Edition Elementary Elements English enlarged equilateral Exercises exterior angle figure four French Geography given point given rectilineal given straight line gnomon Grammar greater Greek half History improved interior isosceles join late Latin less likewise LONGMAN Maps Master Mathematical meet Notes opposite opposite angle parallel parallelogram perpendicular Post Practical produced PROP Proposition proved Questions Reading rectangle contained rectilineal angle right angles Schools selected separately sides sides BA square of AC Take THEOR third triangle ABC twice the rectangle unequal Valpy's wherefore whole
Side 18 - If two triangles have two sides of the one equal to two sides of the...
Side 51 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 109 - ... subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle ACB, and from the point A let AD be drawn perpendicular to BC produced.
Side 53 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line E iR.
Side 76 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 34 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC. And in like manner, it may be demonstrated, that no other can be in the same straight line with it but BD, which therefore is in the same straight line with CB.
Side 11 - LET it be granted that a straight line may be drawn from any one point to any other point.