## The Elements of Geometry, Symbolically Arranged |

### Inni boken

Resultat 1-5 av 5

Side 15

Let AB and AC be

. Constr . In BD take any pt . F ; from AE , the greater , Prop . 3 . cut off AG = AF ;

join FC , GB . Constr . JAF = AG , * AB = AC , Hyp . and _ FAG common to As AFC

...

Let AB and AC be

**prod**. to D and E . Then L ABC = L ACB , and % CBD = _ BCE. Constr . In BD take any pt . F ; from AE , the greater , Prop . 3 . cut off AG = AF ;

join FC , GB . Constr . JAF = AG , * AB = AC , Hyp . and _ FAG common to As AFC

...

Side 25

XV . THEOR . 16 . 1 Eu . If one side of a triangle be produced , the exterior angle

is greater than either of the interior opposite angles . Let ABC be a A , and the

side BC be

XV . THEOR . 16 . 1 Eu . If one side of a triangle be produced , the exterior angle

is greater than either of the interior opposite angles . Let ABC be a A , and the

side BC be

**prod**. to D ; then the ext . L ACD > L CBA or < BAC , the int . oppo . Side 29

... less than the other two sides of the triangle , but shall contain a greater angle .

Let ABC be a A ; from B , C , the ends of the side BC , draw BD , CD , from the

point D within the A ; then BD + DC < BA + AC , and 2 BDC > _ BAC . Α

... less than the other two sides of the triangle , but shall contain a greater angle .

Let ABC be a A ; from B , C , the ends of the side BC , draw BD , CD , from the

point D within the A ; then BD + DC < BA + AC , and 2 BDC > _ BAC . Α

**Prod**.**Prod**. Side 30

+ EC . Prop . 19 . In A CE . : CE + ED > CD , add DB to each ; i . EC + BE > CD +

DB . But it has been proved BA + AC > BE + EC , much more then is BA + AC ...

**Prod**.**Prod**. BD to E . A ABE , BA + AE > BE , add EC to each ; : . BA - - AC > BE+ EC . Prop . 19 . In A CE . : CE + ED > CD , add DB to each ; i . EC + BE > CD +

DB . But it has been proved BA + AC > BE + EC , much more then is BA + AC ...

Side 85

And : : AC is bisected in E and

but EC = EB , . . AD . DC + EB = EDP ; And since _ EBD = rt . L , ED = EB * + DB

% , Prop . 39 . . . AD . DC + EBP = EB + DB : take away EB ' which is common ...

And : : AC is bisected in E and

**prod**. to D , : . AD . DC + EC % = ED , Prop . 45 .but EC = EB , . . AD . DC + EB = EDP ; And since _ EBD = rt . L , ED = EB * + DB

% , Prop . 39 . . . AD . DC + EBP = EB + DB : take away EB ' which is common ...

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The Elements of Geometry, Symbolically Arranged Great Britain. Admiralty Uten tilgangsbegrensning - 1846 |

The Elements of Geometry, Symbolically Arranged Great Britain Admiralty Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

_ ABC ABCD angle contained base base BC bisect called centre circle circumference coincides common Constr descr described diam diameter dist divided draw equal equal angles equiangular equilat expressed extremities falls figure given point given straight line gnomon greater half interior isosceles join less Let ABC line drawn manner mean meet oppo opposite angle opposite sides parallel parallelogram pass perpendicular plane polygon PROB prod produced Prop proportional proposition proved quantities ratio rect rectangle contained rectilineal remain right angles segments shown sides square THEOR touch triangle unequal Wherefore whole

### Populære avsnitt

Side 58 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 32 - 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 60 - 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 36 - Wherefore, if a straight line, &c. QB D. PROPOSITION XXVIII. THEOB.—-If a straight line, falling upon two other straight lines, make the exterior angle equal to...

Side 61 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.

Side 21 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.

Side 37 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...

Side 3 - 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.

Side 77 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.

Side 19 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.