Some Propositions in Geometry: In Five Parts |
From inside the book
Results 1-5 of 19
Page 22
... arc is greater than its sine is the tenth part of the arc length 139 Three Modes of Demonstration - Direct Geometrical Proof , Trigo- nometrical Proof , Inductive Reasoning on direct Evidence . 139 Trigonometrical Demonstration · 140 ...
... arc is greater than its sine is the tenth part of the arc length 139 Three Modes of Demonstration - Direct Geometrical Proof , Trigo- nometrical Proof , Inductive Reasoning on direct Evidence . 139 Trigonometrical Demonstration · 140 ...
Page 39
... 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 cut the perpendicular , and , from the point in which it cuts the perpendicular to the extremity ...
... 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 cut the perpendicular , and , from the point in which it cuts the perpendicular to the extremity ...
Page 40
... length . With centre a and radius ad describe the arc df , cutting the perpendicular in ƒ . Draw the chord fd ( of the arc ) , and bisect it in c ; join a c . Then must the line a c be the mean propor- tional between a b the lesser and ...
... length . With centre a and radius ad describe the arc df , cutting the perpendicular in ƒ . Draw the chord fd ( of the arc ) , and bisect it in c ; join a c . Then must the line a c be the mean propor- tional between a b the lesser and ...
Page 62
In Five Parts John Harris. coincident with the centre of the circle ) the arc ... arc intercepted between the arms standing on the circumference is twice as ... length . From the extremity E cut off one - third of the radius EA in the ...
In Five Parts John Harris. coincident with the centre of the circle ) the arc ... arc intercepted between the arms standing on the circumference is twice as ... length . From the extremity E cut off one - third of the radius EA in the ...
Page 63
... length of Ca , equal to da . Produce also the radius Cb through 6 , making b B , the production of Cb , equal to a A. With centre a and radius AC describe the arc cy intercepting the circumference of the circle in y Join Cy ELEMENTARY ...
... length of Ca , equal to da . Produce also the radius Cb through 6 , making b B , the production of Cb , equal to a A. With centre a and radius AC describe the arc cy intercepting the circumference of the circle in y Join Cy ELEMENTARY ...
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...