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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Libro 1
Visualizzazione completa - 1853
ABC is equal ABCD according adjacent angle ABC angle ACB angle BAC base bisected centre circle ABC circumference cloth coincide common const described diagonal divided double draw drawn edition equal angles equal Ax equimultiples exterior angle extremities fall figure fore fourth given given straight line greater half Hence homologous hyps included angle interior join less Let ABC magnitudes manner meet multiple opposite sides pair parallel parallelogram pass perpendicular plane polygon produced PROP proportional proved radius ratio respectively equal right angles segment shewn sides sides BC similar square square of AC taken THEOR thing are equal third triangle ABC unequal whole
Pagina 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...
Pagina 16 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Pagina 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.
Pagina 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.
Pagina 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.
Pagina 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.
Pagina 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.
Pagina 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.