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

### Dentro del libro

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Página 8

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**angle BAC**is equal ( Hyp . ) to the angle EDF Also , the point C shall coincide with the point F , because AC ( Hyp . ) is equal to DF . But the point B was proved to coincide with the point E. Therefore the base BC shall coincide with ... Página 10

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**angles**ECD , FDC upon the other side of the base CD are equal ( I. 5 ) to one another . But the**angle**ECD is greater ... (**BAC**) which is contained by the two sides of the one is equal to the**angle**( EDF ) contained by the two sides equal ... Página 11

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**angle BAC**coincides with the angle EDF , and is equal ( Ax . 8 ) to it . Therefore if two triangles , & c . Q. E. D. PROP . IX . ( PROBLEM . ) - To bisect a given rectilineal**angle**(**BAC**) ; that is , to divide it into two equal angles ... Página 14

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**angle**BCG . Therefore the**angle**ACD is greater than the**angle**ABC . Therefore , if one side , & c . Q. E. D. PROP ...**BAC**, AC B , as also the two**angles**CAB , ABC , are together less than two right**angles**. Therefore any two**angles**... Página 15

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**angle**DCB . But the**angle**ADB is equal ( I. 5 ) to the**angle**ABD , because the side AB is equal ( Const . ) to the ... (**B A C**) are un- equal , the side opposite to or subtending the greater**angle**( B ) is greater than the side opposite ...### Otras ediciones - Ver todas

The Elements of Plane Geometry; Or, the First Six Books of Euclid. From the ... Vista completa - 1863 |

### Términos y frases comunes

ABC is equal ABCD alternate angle ABC angle BAC angle BCD base base BC bisected centre circle ABC circumference common described divided double draw drawn equal angles equal Ax equal Const equiangular equimultiples exterior angle extremities fore fourth given given straight line greater greater ratio half impossible inscribed interior join less magnitudes manner meet multiple opposite angle parallel parallelogram pass perpendicular PROBLEM.)-To produced proportionals proved Q. E. D. PROP reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown side BC sides similar square square of AC straight line AC Take taken THEOREM.)-If third touches the circle triangle ABC unequal Wherefore

### Pasajes populares

Página 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.

Página 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.

Página 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...

Página 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.

Página 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...

Página 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.

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

Página 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.

Página 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.

Página 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.