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

### Im Buch

Ergebnisse 1-5 von 30

Seite 8

...

...

**base BC**shall coincide with the base EF . For , the point B coinciding with the point E , and the point C with the point F , if the**base BC**does not coincide with the base EF , the two straight lines BC , EF , would enclose a space ... Seite 9

...

...

**base**FC is equal ( I. 4 ) to the**base**GB , and the triangle AFC to the triangle AGB . Also , the remaining angles of ...**BC**is common to both , the two sides DB ,**BC**are equal to the two sides AC , CB , each to each ; and the angle DBC ... Seite 10

... base ( AB ) , and on the same side of it , there cannot be two triangles ... ( BC , EF ) equal ; the angle ( BAC ) which is contained by the two sides of ...

... base ( AB ) , and on the same side of it , there cannot be two triangles ... ( BC , EF ) equal ; the angle ( BAC ) which is contained by the two sides of ...

**base BC**upon the base EF ; then , the point C shall coincide with the point F , be ... Seite 11

...

...

**base BC**coincides with the base EF , the sides BA , AC cannot but coincide with the sides ED , DF . Therefore , the angle BAC coincides with the angle EDF , and is equal ( Ax . 8 ) to it . Therefore if two triangles , & c . Q. E. D. ... Seite 14

...

...

**base**AB is equal ( I. 4 ) to the**base**CF , the triangle AEB to the triangle ...**BC**be bisected , and AC be produced to G , it may be demonstrated that the ...**BC**to D. Because ACD is the exterior angle of the tri- angle ABC , the angle ...### 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.