## Elements of Geometry and Trigonometry |

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**EQUATIONS**OF THE POINT AND STRAIGHT LINE -- of the CONIC SECTIONS of the LINE AND PLANE IN SPACE - also , the discussion of the GENERAL**EQUATION**of the second degree , and of SURFACES OF THE SECOND ORDER . Page 38

... from the first proportion , we have MxQ = NxP , or Nx P = M × Q ; Add each of the members of the last

... from the first proportion , we have MxQ = NxP , or Nx P = M × Q ; Add each of the members of the last

**equation**to , or subtract it from M.P , and we shall have , M.P ± N.P = M.P ± M.Q ; or ( MN ) x P ( P ± Q ) × M. - But M ± N and P ... Page 128

B A D AC2 PC - AP2 , and AB2 - PB2 = AP2 ; we shall have Taking the first

B A D AC2 PC - AP2 , and AB2 - PB2 = AP2 ; we shall have Taking the first

**equation**from the second , and observing that the triangles APC , APB , which are both right angled at P , give AP2 + AP2 = 2AQ2 — 2PQ2 . Page 207

The solution of these

The solution of these

**equations**, when so formed , gives the solution of the problem . No general rule can be given for forming the**equations**. The**equations**must be independent of each other , and their number equal to that of the ... Page 208

hence , Therefore From 1st equ : x = s — y x2 = s2 — Qsy + y2 and By subtracting , 0 = s - 2sy - c2 2sy = s2 ― c2 or PROBLEM I. or Hence , or and From first

hence , Therefore From 1st equ : x = s — y x2 = s2 — Qsy + y2 and By subtracting , 0 = s - 2sy - c2 2sy = s2 ― c2 or PROBLEM I. or Hence , or and From first

**equation**or c2 y = 2s = 4 = AC + 4-9 or x = 5 = BC .### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole