## The school Euclid: comprising the first four books, by A.K. Isbister |

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Resultat 1-5 av 6

Side 142

To inscribe an equilateral and equiangular

To inscribe an equilateral and equiangular

**pentagon**in a given circle . ( References — Prop . I. 9 ; III . 26 , 27 , 29 ; IV . 2 , 10. ) Let ABCDE be the given circle . It is required to inscribe an equilateral and equiangular**pentagon**... Side 144

Then the figure GHKLM shall be the equilateral and equiangular

Then the figure GHKLM shall be the equilateral and equiangular

**pentagon**required . Take the centre F , and join FB , FK , FC , FL , FD . DEMONSTRATION Because the straight line KL touches the circle ABCDE in the point C , to which FC is ... Side 146

9 ) and from the point F , in which they meet , draw the straight lines FB , FA , FE ; draw also the lines FG , FH , FK , FL , and FM perpendicular to the sides of the

9 ) and from the point F , in which they meet , draw the straight lines FB , FA , FE ; draw also the lines FG , FH , FK , FL , and FM perpendicular to the sides of the

**pentagon**; ( 1. 12 ) and from the centre F , at the distance FG ... Side 148

... and the circle described from the centre F , at the distance of one of them , shall pass through the extremities of the other four , wherefore the circle ABCDE is described about the equilateral and equiangular

... and the circle described from the centre F , at the distance of one of them , shall pass through the extremities of the other four , wherefore the circle ABCDE is described about the equilateral and equiangular

**pentagon**ABCDE . Side 150

And if through the points A , B , C , D , E , F , there be drawn straight lines touching the circle , an equilateral and equiangular hexagon shall be described about it , which may be demonstrated from what has been said of the

And if through the points A , B , C , D , E , F , there be drawn straight lines touching the circle , an equilateral and equiangular hexagon shall be described about it , which may be demonstrated from what has been said of the

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The school Euclid: comprising the first four books, by A.K. Isbister Euclides Uten tilgangsbegrensning - 1863 |

The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Ingen forhåndsvisning tilgjengelig - 2009 |

### Vanlige uttrykk og setninger

ABCD angle ABC angle BAC angle BCD angle equal assumed base base BC BC is equal bisect centre circle ABC circumference coincide common constr CONSTRUCTION DEMONSTRATION describe diameter distance divided double draw Edition equal equal to AC equilateral and equiangular exterior angle extremity fall figure four given circle given straight line greater half impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular PROBLEM produced proved Q. E. D. PROP reason rectangle contained References remaining angle right angles segment semicircle shown side BC sides square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle wherefore whole

### Populære avsnitt

Side 141 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 35 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.

Side 71 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...

Side 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Side 61 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...

Side 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.

Side 27 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.

Side 77 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment.

Side 15 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.