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

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Side 7

**Wherefore**from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP . III . - PROBLEM . From the greater of two given straight lines to cut off a part equal to the less . Side 8

therefore AE and C are each of them equal to AD ;

therefore AE and C are each of them equal to AD ;

**wherefore**the straight line AE is equal to C. ( ax . I. ) And therefore from AB , the greater of two straight lines , a part AE has been cut off equal to C , the less . Side 9

therefore AC shall coincide with DF ; and because AC is equal to DF ,

therefore AC shall coincide with DF ; and because AC is equal to DF ,

**wherefore**also the point C shall coincide with the point F. But the point B coincides with the point E ;**wherefore**the base BC shall coincide with the base EF ... Side 11

... CGB ;

... CGB ;

**wherefore**these triangles are equal , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB ; and the angle FBC is equal to the angle CBG . Side 12

... ( 1.4 ) the less equal to the greater , which is absurd . Therefore AB is not unequal to AC , that is AB is equal to AC .

... ( 1.4 ) the less equal to the greater , which is absurd . Therefore AB is not unequal to AC , that is AB is equal to AC .

**Wherefore**, if two angles , & c . R.E.D. Cor . Hence every equiangular triangle is also equilateral . PROP .### Hva folk mener - Skriv en omtale

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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

angle ABC angle BAC angle BCD angle equal assumed base base BC BC is equal bisect centre circle ABC circumference coincide common constr CONSTRUCTION contained DEMONSTRATION describe diameter distance divided double draw Edition equal to AC equilateral and equiangular exterior angle extremity fall figure four given 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 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.