Some Propositions in Geometry: In Five Parts |
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Page 14
... produced line . Az Igfuze L vs. is a produced line of which the extension is endless . That is when the line is said to be produced infinitely in one direction only , the infinite line Las no tenu arī point : ani , when produced ...
... produced line . Az Igfuze L vs. is a produced line of which the extension is endless . That is when the line is said to be produced infinitely in one direction only , the infinite line Las no tenu arī point : ani , when produced ...
Page 39
... Produce , in both directions , the alternate sides of the hexagon , namely , NQ , EF , PM , the productions meeting ... produced in both directions , so that the produced lines meet in three points , the resulting triangle is equilateral ...
... Produce , in both directions , the alternate sides of the hexagon , namely , NQ , EF , PM , the productions meeting ... produced in both directions , so that the produced lines meet in three points , the resulting triangle is equilateral ...
Page 40
... Produce A C through C and from point e , at right angles to Ae , draw e D meeting the production of AC in point D. Then , by similarity of the triangles , AB : AC ( or Ae ) :: AC : AD . Wherefore AD is the third proportional to A B , A ...
... Produce A C through C and from point e , at right angles to Ae , draw e D meeting the production of AC in point D. Then , by similarity of the triangles , AB : AC ( or Ae ) :: AC : AD . Wherefore AD is the third proportional to A B , A ...
Page 41
... produce it through m , and with centre A and radius AD cut the produced line in point n . From point n draw a perpendicular to A D intercepting that line in point E. The line AE is the fourth proportional : for , by similarity of the ...
... produce it through m , and with centre A and radius AD cut the produced line in point n . From point n draw a perpendicular to A D intercepting that line in point E. The line AE is the fourth proportional : for , by similarity of the ...
Page 43
... Produce CA through A , and with centre P and radius PC describe an are cutting the production of CA in B. Join P B. Then because radius PC is twice radius QC , and chord C B is a production of chord C A , the greater arc CB is similar ...
... Produce CA through A , and with centre P and radius PC describe an are cutting the production of CA in B. Join P B. Then because radius PC is twice radius QC , and chord C B is a production of chord C A , the greater arc CB is similar ...
Other editions - View all
Some Propositions in Geometry: In Five Parts (Classic Reprint) John Harris No preview available - 2017 |
Some Propositions in Geometry: In Five Parts Associate Professor University of Alberta Canada John Harris No preview available - 2016 |
Some Propositions in Geometry: In Five Parts (Classic Reprint) John Harris No preview available - 2017 |
Common terms and phrases
arc FM arc q arc-length areally equal centre of description circle's circumference circumscribed connecting arc curvilineal cut off one-third demonstration describe the arc diagonal diameter diff Dinostratus distance divided divisional arc divisional points Draw the chord duplicate ratio entire arc equal angles equals arc equals twice equilateral triangle Euclid's Euclid's Elements geometrical given angle given circle given cube given straight line greater octant half half-arc isosceles triangle Join lesser octant lineal magnitude lineal side manifestly mean proportional number of equal octagon octantal segments one-nth parallelogram point D point g point of bisection polygon Polysection primary arc primary octant PROBLEM Produce Prop quadrantal arc quadratrix radial line rectangle contained regular polygon required number rhombus right angles Scholium semicircle similar triangles sine tangent line terminal point Theorem transverse arc trisect unital increment vertex vertical angle Wherefore
Popular passages
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 73 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
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.
Page 128 - CD the triplicate ratio of that • which AE has to CF. Produce AE, GE, HE, and in these produced take EK equal to CF, EL equal to FN, and EM equal to FR; and complete the parallelogram...