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

### Dentro del libro

Resultados 1-5 de 12

Página 50

...

...

**inscribed**in a circle ( ABCD ) , are together equal to two right angles . Join AC and BD . The angle CAB is equal to the angle CDB ( III . 21 ) , because they are in the same segment CDAB . And the angle ACB is equal to the angle ADE ... Página 54

...

...

**inscribed**in a circle , any two of its opposite angles are equal ( III . 22 ) to two right angles . Therefore the angles ABC and ADC , are equal to two right angles . But ABC has been proved to be less than a right angle . Therefore the ... Página 58

...

...

**inscribed**in another , when all the angular points of the**inscribed**figure are upon the sides of the figure in which it is**inscribed**, each upon each . II . In like manner , one rectilineal figure is said to be described about ... Página 59

...

...

**inscribe**a triangle equiangular to a given triangle ( DEF ) . Draw the straight line GH touching the circle in the ...**inscribed**in the circle ABC . Q. E. F. PROP . III . ( PROBLEM . ) - About a given circle ( ABC ) to describe a ... Página 60

...

...

**inscribe**a circle in a given triangle ( ABC ) . Bisect the angles ABC and BCA by the straight lines BD and CD and let these straight lines meet one another in the point D ( I. 9 ) . from the point D draw DE , DF , and DG per- pendicular ...### Términos y frases comunes

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

### 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.