## The Elements of Geometry, Symbolically Arranged |

### Inni boken

Side 95

the same proportion . Let ABC , DEF be

respectively equal to Zs D , E , F , ea . to ea . ; then shall AB : AC : : DE : DF ; or

AB ...

**Equiangular**triangles have their corresponding sides about the equal angles inthe same proportion . Let ABC , DEF be

**equiangular**As , having Ls A , B , C ,respectively equal to Zs D , E , F , ea . to ea . ; then shall AB : AC : : DE : DF ; or

AB ...

Side 96

Therefore

Def . 3 . pa . 89 . PROP . LXXIV . THEOR . 6 . 6 Eu . Two triangles are

, when an angle in the one is equal to an angle in the other , and the sides about

...

Therefore

**equiangular**triangles , & c . Cor . -**Equiangular**triangles are similar .Def . 3 . pa . 89 . PROP . LXXIV . THEOR . 6 . 6 Eu . Two triangles are

**equiangular**, when an angle in the one is equal to an angle in the other , and the sides about

...

Side 103

As ABD , BCE , are

...

perpendiculars upon the bases from the opposite and equal angles . Let the As ...

As ABD , BCE , are

**equiangular**, . . BC : CE ... As ABÈ , BDC , are**equiangular**: ....

**Equiangular**triangles have their bases in the same ratio as their altitudes , orperpendiculars upon the bases from the opposite and equal angles . Let the As ...

Side 106

Also : , : As ABC , DEF are

ADEF ABIC – ZELF AABC ADEF 2ABIC 2AELF : ut 12 A BIC = Sq . BK = BC 12 A

ELF = Sq . EM = EF AABC DEF . : BC = EF That is A ABC : BC : : ADEF : EF , Prop

.

Also : , : As ABC , DEF are

**equiangular**, AG DH Prop . 81 . BC — EF ; AABCADEF ABIC – ZELF AABC ADEF 2ABIC 2AELF : ut 12 A BIC = Sq . BK = BC 12 A

ELF = Sq . EM = EF AABC DEF . : BC = EF That is A ABC : BC : : ADEF : EF , Prop

.

Side 107

J LA = ZF AB : AE : : FG : FK , jAs ABE , FGK are

LFKG ; Also . . . ZC = LH Hyp . BC : CD : : GH : HI , As BCD , GHI are

Prop . 74 . 1 ZCDB = HIG . Again - IZAED = / FKI . Agam . AEB FKG , : rem .

J LA = ZF AB : AE : : FG : FK , jAs ABE , FGK are

**equiangular**, Prop . 74 . IL AEB =LFKG ; Also . . . ZC = LH Hyp . BC : CD : : GH : HI , As BCD , GHI are

**equiangular**.Prop . 74 . 1 ZCDB = HIG . Again - IZAED = / FKI . Agam . AEB FKG , : rem .

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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.