## 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, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |

### Inni boken

Resultat 1-5 av 5

Side 4

Let ABC be a right angled triangle ; if the hypothenuse BC be made

either of the sides AC will be the fine of the angle ABC opposite to it , and if either

side BA be made radias , the other side AC will be the tangent of the angle ABC ...

Let ABC be a right angled triangle ; if the hypothenuse BC be made

**radius**,either of the sides AC will be the fine of the angle ABC opposite to it , and if either

side BA be made radias , the other side AC will be the tangent of the angle ABC ...

Side 22

therefore AF is the tangent of the arch AC ; and in the rectilineal triangle AEF ,

having a right angle at A , AE will be to the

AEF , ( 1. Pl . Tr . ; ) but AE is the fine of the arch AB , and AF the tangent of the ...

therefore AF is the tangent of the arch AC ; and in the rectilineal triangle AEF ,

having a right angle at A , AE will be to the

**radius**as Ar to the tangent of the angleAEF , ( 1. Pl . Tr . ; ) but AE is the fine of the arch AB , and AF the tangent of the ...

Side 24

of the angle ECF opposite to it , that is , in the triangle ABC , the co - fine of the

hypothenufe BC is to the

tangent of the angle ACB . Q. E. D. COR . 1. Of these three , viz . the hypothen

use ...

of the angle ECF opposite to it , that is , in the triangle ABC , the co - fine of the

hypothenufe BC is to the

**radius**, as the co - tangent of the angle ABC is to thetangent of the angle ACB . Q. E. D. COR . 1. Of these three , viz . the hypothen

use ...

Side 27

The rectangle contained by the

the rectangle contained by the co - lines of the the opposite parts . These rules

are demonstrated in the following manner . First , Let either of the sides , as BA ...

The rectangle contained by the

**radius**, and the fine of the middle part is equal tothe rectangle contained by the co - lines of the the opposite parts . These rules

are demonstrated in the following manner . First , Let either of the sides , as BA ...

Side 35

... CA is to AE as AB , that is , twice AE to AF ; and by halving the antecedents ,

half of the

versed sine of the arch AB , Wherefore by 16. 6. the proposition is manifeft .

PROP .

... CA is to AE as AB , that is , twice AE to AF ; and by halving the antecedents ,

half of the

**radius**CA is to AE the line of the arch AD , as the fame AE to AF theversed sine of the arch AB , Wherefore by 16. 6. the proposition is manifeft .

PROP .

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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 156 - 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 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.

Side 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 92 - 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 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Side 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.

Side 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

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.

Side 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.

Side 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...