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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text, Based ...
Uten tilgangsbegrensning - 1853
ABCD according angle ACB angle BAC angles ABC angular points applied base bisected centre circle ABC circumference coincide common const defn described diagonal divided double draw drawn equal angles equal Ax equimultiples exterior angle extremities fall figure fore four magnitudes fourth given straight line greater hence hyps included angle interior Join kind less Let ABC magnitudes manner meet multiple opposite sides pair parallel parallelogram pass perpendicular plane polygon produced PROP proportional proved ratio remaining respectively equal right angles segment shewn sides similar similarly square straight line taken THEOR thing are equal third third angle touch triangle ABC unequal whole
Side 39 - 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...
Side 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Side 5 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw, from the point A, a straight line equal to BC.
Side 11 - 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 another, and likewise those which are terminated in the other extremity.
Side 105 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Side 118 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Side 66 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 6 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.