Some Propositions in Geometry: In Five Parts |
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Page 25
... Join Ef and De . The point C , in which the three lines Ag , Bf , De , intersect , is equidistant from the angle points E and D , and is therefore the lateral centre of the triangle A E D. D .. ' 2012 124 adera trange Bag 2 . • PART ...
... Join Ef and De . The point C , in which the three lines Ag , Bf , De , intersect , is equidistant from the angle points E and D , and is therefore the lateral centre of the triangle A E D. D .. ' 2012 124 adera trange Bag 2 . • PART ...
Page 27
... Join the last divisional point in the second line to the extremity of the given line opposite to that at which the two lines meet ; and from each successive divisional point in the second line draw a line , parallel to the first line of ...
... Join the last divisional point in the second line to the extremity of the given line opposite to that at which the two lines meet ; and from each successive divisional point in the second line draw a line , parallel to the first line of ...
Page 28
... joining the divisional points , the triangle will be divided into triangles similar to itself , equal each to each , and equal in number to the product of the number of the divisional parts of each of the mides multiplied by ite1f ...
... joining the divisional points , the triangle will be divided into triangles similar to itself , equal each to each , and equal in number to the product of the number of the divisional parts of each of the mides multiplied by ite1f ...
Page 30
... Join ef cutting the line Ab in the point a , and from ƒ draw ƒg perpendicular to B D. Because fg is perpendicular to BD , and point g bisects b D , the part fC is one - third of ƒ B , and the part e C one - third of e D ( Prop . 6 ) ...
... Join ef cutting the line Ab in the point a , and from ƒ draw ƒg perpendicular to B D. Because fg is perpendicular to BD , and point g bisects b D , the part fC is one - third of ƒ B , and the part e C one - third of e D ( Prop . 6 ) ...
Page 31
... join A C , DC , E C. With centre C and radius C A describe the circle ADE . The circle A D E is circumscribed about the equilateral triangle A D E. Because C is the centre of the equilateral triangle ADE ( Def . 19 ) , and equidistant ...
... join A C , DC , E C. With centre C and radius C A describe the circle ADE . The circle A D E is circumscribed about the equilateral triangle A D E. Because C is the centre of the equilateral triangle ADE ( Def . 19 ) , and equidistant ...
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...