Some Propositions in Geometry: In Five Parts |
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Page 6
... difference between the two systems- " Geometry and Metaphysics , " it does not nearly comprise the whole difference ; for , in its mode of procedure , Geometry loves Law and Order , and Metaphysics detests both . Geometry delights in ...
... difference between the two systems- " Geometry and Metaphysics , " it does not nearly comprise the whole difference ; for , in its mode of procedure , Geometry loves Law and Order , and Metaphysics detests both . Geometry delights in ...
Page 39
... difference between the two lines , and from the point of section draw a perpendicular of indefinite length . With the opposite extremity of the greater line as a centre of description and the line itself as a radius , describe an arc to ...
... difference between the two lines , and from the point of section draw a perpendicular of indefinite length . With the opposite extremity of the greater line as a centre of description and the line itself as a radius , describe an arc to ...
Page 47
... difference between the diagonal and twice the side of the square , ‡ equals the rectangle contained by the diagonal and the difference between the side of the square and the diagonal . Corollary 2. And ( for the same reason ) it follows ...
... difference between the diagonal and twice the side of the square , ‡ equals the rectangle contained by the diagonal and the difference between the side of the square and the diagonal . Corollary 2. And ( for the same reason ) it follows ...
Page 48
... difference between the square on the greater side and the square on the diagonal of a rectangle equals the square on the lesser side . ( See Prop . 31. ) * See Prop . 34 . PROP . XXXI . THEOREM . The square on the 48 SOME PROPOSITIONS ...
... difference between the square on the greater side and the square on the diagonal of a rectangle equals the square on the lesser side . ( See Prop . 31. ) * See Prop . 34 . PROP . XXXI . THEOREM . The square on the 48 SOME PROPOSITIONS ...
Page 49
... difference between the square on bd and the square on bc . ( Prop . 30A , Cor . 1 ) . But the rectangle bd dp is the rectangle b q , which has been shown to equal the square a bƒe , wherefore the square on the lesser side , a b , of the ...
... difference between the square on bd and the square on bc . ( Prop . 30A , Cor . 1 ) . But the rectangle bd dp is the rectangle b q , which has been shown to equal the square a bƒe , wherefore the square on the lesser side , a b , of the ...
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...