## The Circle and Straight Line, Volum 2 |

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actual appears applied arc B. M. arc-length arrives become belonging bisected boundary breadth centre chord circle circumference circumscribed coincidence complete compounded considered construction contained continued curvature decimal definite demonstration described diameter diff difference distance divided division divisional draw drawn duplicated elements equal in length Euclid's evident examination expressed extremity fact figure follows fraction Geometry given greater greater arc half half-quadrant illustration included increased indicated inscribed intercepting intersect knowledge length less lesser line B. E. magnitude means measure method necessarily objection obtain octant octuple arc one-tenth perpendicular point of contact polygon primary produced Prop proportion proposition quadrant quantitive radius A.B. ratio reason relation relative remaining respectively result rolled secant shown side similar sine sine-length solid square straight line successive superficies supposed surface taken tangent terminal theorem third thousand triangle true ultimate versed sine

### Populære avsnitt

Side 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...

Side 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.

Side 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.

Side 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 : :

Side 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...

Side 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...

Side 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.

Side 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...

Side 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.

Side 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.