## Elements of geometry, containing the first two (third and fourth) books of Euclid, with exercises and notes, by J.H. Smith, Del 2 |

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Resultat 1-5 av 12

Side 124

**Find**o the centre of the O. III . 1 , Cor . Join 0A , OD , OB . I. 4 , Then : _OAB = LOBA , and LODB is greater than _OAB , 1. 16 . : LODB is greater than ZOBA ; and : OB is greater than OD . I. 19 , :: the distance of D from O is less ... Side 126

But if neither pass through the centre ,

But if neither pass through the centre ,

**find**the centre 0 , and join OE . Then : OE , passing through the centre , bisects AB , .. LOEA is a rt . L. III . 3 . And :: OE , passing through the centre , bisects CD , :: LOEC is a rt . Side 136

**Find**( the centre of O ABC , and join 0A . Then must the centre of O ADE lie in the radius OA . For if not , let P be the centre of ADE . Join OP , and produce it to meet the Oces in D and B. Then ::: P is the centre of ADE , and from 0 ... Side 145

C.

C.

**Find**0 the centre , and join OC . Then must OC be I to DE . For if it be not , draw OBF 1 to DE , meeting the Oce in B. Then :: OFC is a rt . angle , . : OCF is less than a rt . angle , 1. 17 . and :: OC is greater than OF . I. 19 . Side 170

**Find**a point in the diameter produced of a given circle , from which , if a tangent be drawn to the circle , it shall be equal to a given straight line . 15. Two equal circles intersect in the points A , B , and through B a straight ...### Hva folk mener - Skriv en omtale

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Elements of geometry, containing the first two (third and fourth ..., Del 1 Euclides Uten tilgangsbegrensning - 1871 |

Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |

Elements of Geometry, Containing the First Two (Third and Fourth) Books of ... Euclides Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

ABCD base Book centre chord circles touch circumference coincide common construction cutting the circle Describe a circle described diagonals diameter difference distance divided double draw equal equal circles equiangular extremities fall figure Find formed four given circle given point given straight line greater Hence hexagon inscribed join less Let ABC lies line be drawn line drawn meet middle points NOTE opposite sides parallel parallelogram pass perpendicular point of contact PROBLEM produced PROPOSITION prove Q. E. D. Ex quadrilateral radius rect regular pentagon required to inscribe respectively right angles segment semicircle shew shewn sides Similarly square subtended sum of 28 tangents THEOREM third touch touch the circle triangle triangle ABC twice

### Populære avsnitt

Side 152 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.

Side 168 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 161 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Side 132 - If a point be taken within a circle, from which there fall more than two equal straight lines to the circumference, that point is the centre of the circle. Let...

Side 163 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.

Side 177 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw (1 7. 3.) the straight line G AH touching the circle in the point A, and. at the point A, in the straight line AH, make (23.

Side 184 - ABD is described, having each of the angles at the base double of the third angle.

Side 207 - Upon the same straight line, and upon the same side of it, there cannot be two similar segments of circles, not coinciding with one another. If it be possible. let the two similar segments of circles, viz. ACB' ADB be upon the same side of the same straight line AB, not coinciding with one another.

Side 203 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.

Side 183 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.