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Some Propositions in Geometry: In Five Parts
Associate Professor University of Alberta Canada John Harris
No preview available - 2016
applied arc-length areal arms base becomes belonging Bisect called centre chord circle's circumference circumscribed connecting Construction contained cube definite demonstration describe diagonal diameter diff difference distance divided divisible draw Draw the chord drawn duplicate entire equal equal angles equilateral triangle Euclid's evident extremity figure follows four geometrical given angle given circle greater half increased inscribed intercepting isosceles triangle Join less lesser lesser octant lineal magnitude mean proportional meeting method nine octagon octant one-nth one-third parallel parallelogram perpendicular Plate point g polygon primary arc PROBLEM Produce Prop proposition quadrantal radial radius ratio rectangle regular remaining respectively respondent right angles segments shown side similar sine square straight line terminal Theorem third transverse arc Trisection twice ultimate unital vertex vertical angle Wherefore whole
Page 70 - The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced the angles on the other side of the base shall be equal to one another.
Page 41 - To find a fourth proportional to three given straight lines. Let A, B, C be the three given straight lines ; it is required to find a fourth proportional to A, B, C. Take two straight lines DE, DF, containing any angle Book VI. EDF ; and upon these make DG equal to A, GE equal to B, and DH equal to C : and having joined GH, draw EF parallel...
Page 40 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.
Page 50 - Three numbers may be in proportion when the first is to the second as the second is to the third.
Page 106 - PKOPOSITION 46. PROBLEM. To describe a square on a given straight line. Let AB be the given straight line : it is required to describe a square on AB.
Page 29 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 74 - ... To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Page 45 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.