## The Elements of Geometry, Symbolically Arranged |

### From inside the book

Results 1-5 of 13

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**oppo**. " " opposite . ence . post . cr . centre . const . 99 construction . prod . 99 def . definition . 99 prop . 99 descr . describe . 99 pt . 99 diam . diameter . 99 rect . 29 postulate . produce . produced . proposition . point ... Page 17

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**oppo**. side of the base will follow from Prop . 12 . PROP . VI . THEOR . 6. 1 Eu . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to the equal angles , shall be equal to one another ... Page 19

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**oppo**. sides of CA. Join BD . Hyp . In ABD :: △ In Δ BCD AB = AD , ABD = ADB ; BC = CD , Prop . 5 . Hyp . :: ≤ CBD = △ CDB , Prop . 5 . and △ CBA CDA . Ax . 2 , 3 . AB , BC = AD , DC , ea . to ea . Hyp . and incl . CBA = incl ... Page 23

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**oppo**. sides of AB , make the adj . s ABC + ABD 2 rt . Zs ; then shall BD be in the same straight line with BC . = Α C B E D If BD be not in the same str . line with CB , let BE be in the same str . line with it ; then : str . line AB ... Page 25

... ABC be a A , and the side BC be prod . to D ; then the ext . △ ACD > △ CBA or BAC , the int .

... ABC be a A , and the side BC be prod . to D ; then the ext . △ ACD > △ CBA or BAC , the int .

**oppo**. A s . F B D C G Bisect AC in E. Join BE and prod . it to F. C Prop . 9 . Prop . 3 . Constr . Prop . 14 . PROP . XV . 25.### Other editions - View all

### Common terms and phrases

2ndly ABCD AC² angle contained angle equal base BC CB² centre circle circumference coincides Constr descr diam diameter dist divided equal angles equiangular equilat exterior angle figure given point given str given straight line gnomon greater isosceles triangle join Let ABC Let str Let the str line be drawn meet number of equal oppo opposite angle opposite sides parallel parallelogram perpendicular polygon PROB prod Prop rect rectangle contained rectilineal right angles right-angled triangle semi sides equal square THEOR touch trapezium Wherefore whole fig Нур

### Popular passages

Page 60 - 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.

Page 34 - 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...

Page 62 - 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...

Page 38 - 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...

Page 63 - 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.

Page 23 - 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.

Page 39 - 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...

Page 5 - 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.

Page 79 - 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.

Page 21 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.