## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |

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6 ' N. B. When several

6 ' N. B. When several

**angles are**at**one**point B , any**one**of them is expressed by three letters , of which the letter ... the**angle**meet**one another**, is put between the**other two**letters , and**one**of these**two**is somewhere upon**one**of ... Página 8

The Errors, by which Theon, Or

The Errors, by which Theon, Or

**Others**,**Have**Long Ago Vitiated These Books,**are**Corrected and Some of Euclid's ... F**two triangles have two sides of the one equal to two sides**of the**other**, each to each ; and**have**likewise the**angles**... Página 9

D А BAC

D А BAC

**equal**to the**angle**EDF . the base BC shall be**equal**to the base EF ; and the triangle ABC to the triangle DEF ... Therefore if**two triangles have two sides of the one equal to two sides**of the**other**, each to each , and**have**... Página 10

... the

... the

**angle**FAG common to the**two triangles**AFC , AGB ; therefore the base А FC is**equal**to the base GB , and the triangle AFC to the triangle AGB ; and the remaining**angles of the one are equal**to the remaining**angles of the other**... Página 11

b UPON Let ABC be a triangle

b UPON Let ABC be a triangle

**having**the**angle**ABC**equal**to the**angle**Book I. ACB ; the side AB is also**equal**to the side ... be**two triangles**that**have**their sides which**are**terminated in**one**extremity of the base equai to**one another**...### Comentarios de la gente - Escribir un comentario

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added alſo altitude angle ABC angle BAC baſe BC is given becauſe Book caſe circle circle ABCD circumference common cone contained cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſm produced PROP proportionals Propoſition pyramid reaſon rectangle remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſquare ſquare of BC taken THEOR theſe third thro triangle ABC wherefore whole

### Pasajes populares

Página 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Página 163 - 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.

Página 48 - 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.

Página 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...

Página 105 - 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...

Página 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.

Página 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

Página 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Página 47 - 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.

Página 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.