## Elements of Geometry;: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |

### Inni boken

Side 12

, shall also be

BC

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**PROP**.**VI**.**THEOR**. F**two**angles of a**triangle**be**equal**to**one another**, , angles, shall also be

**equal**to**one another**. Let ABC be a**triangle having**the**angle**ABC

**equal**to the**angle**ACB ; the side AB**is**also**equal**to the side AC . For ,**if**ABbe not

**equal**to AC ,**one**of them**is**greater than a 3. I. the**other**: Let AB be the ... Side 15

are terminated in

likewise

IX . PROB . To bisect a given rectilineal

are terminated in

**one**extremity of the base**equal**to**one**Buok'I .**another**, andlikewise

**their**fides terininated in the**other**...**if two triangles**, & c . Q. E. D.**PROP**.IX . PROB . To bisect a given rectilineal

**angle**, that**is**, to divide it into two**equal**... Side 164

I. reBook

the

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**VI**. Let the triangles ABC , DEF**have**the**angle**BAC in the**one equal**tothe

**angle**EDF in the**other**, and the fides about those ... Wherefore ,**if two****triangles**, & c . Q. E. D. d11.3 .**PROP**. Book**VI**. PRO P. VII .**THEOR**.**IF**164ELEMENTS.

Side 178

А CE Book

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because . as BC

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**VI**. bout**two equal**angles reciprocally proportional , are**equal**to**one**€ 15.6 .

**another**e : therefore the**triangle**ABG**is equal**to the**triangle**DEF ; andbecause . as BC

**is**to EF , so D EF to BG ; and that**if**three straight lines be ... SM**PROP**. XX .**THEOR**. IMILAR polygons may be divided into the same number ofsimilar

**triangles**,**having**the same ... the**triangles**ABE , FGL**have an one equal**to

**an angle**in the**other**, and**their**fides about FGHKL**angle**in thes Book**VI**. d 22. 5 .

Side 197

BD

the

ABD

the

arch of a circle be bisected , and from the extremities of the arch , and from the

point of ...

BD

**is equal**Book**VI**. to the**two**rectangles AB. ... Make the**angle**ABE**equal**tothe

**angle**DBC ; add to**each**of these the common**angle**EBD , then the**angle**ABD

**is**... 3 , the**angle**BCE , because they are in the fame segment ; thereforethe

**triangle**ABD**is**equiangular to the**triangle**...**6**.**PROP**. E.**THEOR**.**IF**F**an**arch of a circle be bisected , and from the extremities of the arch , and from the

point of ...

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Elements of Geometry: Containing the First Six Books of Euclid with a ... Euclid,Formerly Chairman Department of Immunology John Playfair,John Playfair Ingen forhåndsvisning tilgjengelig - 2015 |

### Vanlige uttrykk og setninger

ABCD alſo altitude angle ABC angle BAC arch baſe becauſe biſected Book caſe centre circle circle ABC circumference coincide common cylinder definition demonſtrated deſcribed diameter difference divided draw drawn equal equal angles equiangular Euclid extremity fall fame fides firſt folid fore four fourth given given ſtraight line greater half inſcribed join leſs Let ABC magnitudes meet multiple muſt oppoſite parallel parallelogram perpendicular plane polygon priſm produced PROP proportionals propoſition proved Q. E. D. PROP radius ratio rectangle contained remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſin ſolid ſpherical ſquare ſtraight line ſuch ſum taken tangent THEOR theſe third thoſe touches triangle ABC wherefore whole

### Populære avsnitt

Side 27 - 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 172 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 42 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.

Side 84 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...

Side 106 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.

Side 22 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA : the side AC is likewise greater than the side AB. For, if it be not greater, AC must...

Side 64 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...

Side 166 - IN a right angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another. Let ABC be a right angled triangle, having the right angle BAC ; and from the point A let AD be drawn perpendicular to the base BC : the triangles ABD, ADC are similar to the whole triangle ABC, and to one another.

Side 54 - 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...

Side 2 - 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.