The Circle and Straight Line, Τόμος 2J. Lovell, 1875 |
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applied arc B. M. arc containing arc of 15 arc of 30 become in contact bisecting the quadrant boundary breadth centre chord circumference circumscribed polygon Co-secant Co-sine Co-tangent compounded construction curvature cyclal decimal circles definite demonstration describe the quadrant diameter diff difference distance divided divisional point drawn equal division equal divisional equal in length Euclid's Euclid's Elements evident fractional arc given straight line greater arc half quadrant half-quadrant Ideal Philosophy illustration increased intercepting the line intersect JOHN HARRIS KUKL Legendre Legendre's lesser arc line B. E. line B.D. line M.S. magnitudinal method nine equal nine-tenths octant B.M. octuple arc perpendicular point of bisection point of contact primary arc Prop proposition quantitive value radial duplication radius A.B. ratio relation right angles rolled Scholium secant Sextuple Arc similar arcs sine and arc sine and arc-length sine S. R. sine-length solid square superficies surface terminal extremity theorem triangle ultimate sine versed sine Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 61 - It is necessary to consider a solid, that is, a magnitude which has length, breadth, and thickness, in order to understand aright the definitions of a point, line and superficies ; for these all arise from a solid, and exist...
Σελίδα 62 - KBCL, which is contiguous to it, this boundary BC is called a line, and has no breadth : For, if it have any, this must be part either of the breadth of H (> ** " N the superficies ABCD, or of the superficies KBCL, or part of each of them.
Σελίδα 62 - AG, remains still the same as it was. Nor can it be a part of the thickness of the solid AG : because if this be removed from the solid BM, the superficies BCGF, the boundary of the solid BM, does nevertheless remain ; therefore the superficies BCGF has no thickness, but only length and breadth.
Σελίδα 38 - CD : CM. Again, the triangles CAM, CME, having the common vertex M, are to each other as their bases CA, CE ; they are likewise to each other as the polygons A' and B of which they form part ; hence A' : B : :
Σελίδα 63 - For if it have any, this length must either be part of the length of the line AB, or of the line KB. It is not part of the length of KB ; for if the line KB be removed from AB, the point B, which is the extremity of the line AB, remains the same as it was : nor is it part of the length of the line AB ; for, if AB be removed from the line KB, the point B, which is the extremity of the line KB, does nevertheless remain : therefore the point B has no length : and because a point is in a line, and a...
Σελίδα 40 - Sch.), that of the circumscribed square will be equal to the diameter 2 ; hence the surface of the inscribed square is 2, and that of the circumscribed square is 4. Let us therefore put...
Σελίδα 38 - ... regular inscribed and circumscribed polygons having double the number of sides. Let AB be a side of the given inscribed polygon ; EF, parallel to AB, a side of the circumscribed polygon, and C the centre of the circle.
Σελίδα 41 - ... circle is between the two, it cannot, strictly speaking, differ from either so much as they do from each other ; so that the number 3.1415926 expresses the area of a circle whose radius is 1, correctly, as far as seven places of decimals. Some doubt may exist, perhaps, about the last decimal figure, owing to errors proceeding from the parts omitted ; but the calculation has been carried on with an additional figure, that the final result here given might be absolutely correct even to the last...
Σελίδα 40 - ... circumscribed polygon* and since those polygons agree as far as a certain place of decimals, must also agree with both as far as the same place.
Σελίδα 61 - BM, or a part of the thickness of each of them. It cannot be a part of the thickness of the solid BM ; because, if this solid be removed from the solid AG, the superficies BCGF, the boundary of the solid AG, remains sti'l the same as it was.