## The elements of plane geometry; or, The first six books of Euclid, ed. by W. Davis1863 |

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**pass**through the centre , the latter is cut at right angles : and , conversely , if it be cut at right angles it is bisected . E Take E the centre of the circle ( III . 1 ) , and join EA and EB . Because AF is equal to FB ( Hyp ... Seite 41

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**pass**through the centre . But if neither of them**pass**through the centre , take F the centre of the circle ( III . 1 ) , and join EF . B E F T A Because FE , a straight line passing through the A centre , bisects ( Hyp . ) another AC ... Seite 44

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**passes**through that point . For if the straight line joining their centres do not**pass**through the point A , let it**pass**otherwise , possible , as FGDH , let F be the centre of the circle ABC , and G the centre of the circle ADE . Join ... Seite 45

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**pass**through the point A. Therefore , if two circles , & c . Q. E. D. H PROP . XIII . ( THEOREM . ) - One circle ...**passes**through ( III . 11 ) the points of contact B E H B D and D. Therefore G H coincides with DB . But GH is also at ... Seite 46

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**pass**through the centre , at right angles ( III . 3 ) , AB is bisected at F. Therefore AF is equal to FB , and AB double of AF . For the same reason , CD is double of CG . But AB is equal ( Hyp . ) to CD . Therefore AF is equal ( I. Ax ...### Häufige Begriffe und Wortgruppen

ABC is equal ABCD adjacent angles alternate angle angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF arc BC base BC bisected centre circle ABC circumference double equal angles equal Ax equal Const equal Hyp equal to F equals add equiangular equimultiples exterior angle four magnitudes fourth G and H given straight line gnomon greater ratio greater than F interior and opposite join less multiple opposite angle parallel parallelogram parallelogram BD perpendicular PROBLEM.)-To produced Q. E. D. PROP rectangle contained remaining angle right angles segment side BC square of AC straight line AB straight line AC THEOREM.)-If three straight lines touches the circle triangle ABC triangle DEF twice the rectangle whole angle

### Beliebte Passagen

Seite 3 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. VIII. A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.

Seite 4 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.

Seite 67 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Seite 12 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Seite 93 - From this it is manifest, that the perpendicular drawn from the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base; and also that each of the sides is a mean proportional between the base, and...

Seite 68 - This word is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which the second has to the fourth ; or that the first is to the third as the second to the fourth : as is shown in Prop.

Seite 5 - LET it be granted that a straight line may be drawn from any one point to any other point.

Seite 88 - From this it is plain, that triangles and parallelograms that have equal altitudes, are to one another as their bases. Let the figures be placed so as to have their bases in the same straight line; and having drawn perpendiculars from the vertices of the triangles to the bases, the straight line which joins the vertices is parallel to that in which their bases are, (I.

Seite 69 - This term is used when the first magnitude is to the second of the first rank, as the last but one is to the last of the second rank; and as the second is to the third of the first rank, so is the last but two to the last but one of the second rank; and as the third is to the fourth of the first rank, so is the third from the last to the last but two of the second rank; and so on in a cross order: and the inference is as in the 18th definition.

Seite 21 - ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.