## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |

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Side 253

... case of this; being the same as this proposition, when the given ratio is a ratio

of equality. PROP. XXIV. PROB. To draw a common

Let BDC, FHG be given circles; it is required to draw a common

... case of this; being the same as this proposition, when the given ratio is a ratio

of equality. PROP. XXIV. PROB. To draw a common

**tangent**to two given circles.Let BDC, FHG be given circles; it is required to draw a common

**tangent**to them. Side 254

one another, there will be two exterior

the circles touch the other internally, they can have only one common

and this passes through their point of contact: and, lastly, if one of them lie wholly

...

one another, there will be two exterior

**tangents**, but no transverse one: if one ofthe circles touch the other internally, they can have only one common

**tångent**,and this passes through their point of contact: and, lastly, if one of them lie wholly

...

Side 295

If a straight line touch a circle at one extremity of an arc, the part of it intercepted

between that extremity and the diameter produced, passing through the other, is

called the

If a straight line touch a circle at one extremity of an arc, the part of it intercepted

between that extremity and the diameter produced, passing through the other, is

called the

**tangent**of the arc, or of the angle which it measures; and the straight ... Side 296

H E e sine of this arc and angle; FI, or its equal CG, their cosine; AG their versed

sine, and DI their coversed sine; A H their

cotangent, and CK their cosecant. From these definitions we derive immediately ...

H E e sine of this arc and angle; FI, or its equal CG, their cosine; AG their versed

sine, and DI their coversed sine; A H their

**tangent**, and CH their secant; DK theircotangent, and CK their cosecant. From these definitions we derive immediately ...

Side 297

So likewise are their cosines,

cosecants. Let AF be an arc, FG, A H its sine and

and cotangent. Make the angle BCM equal to ACF; draw the perpendicular MO; ...

So likewise are their cosines,

**tangents**, and cotangents, and their secants andcosecants. Let AF be an arc, FG, A H its sine and

**tangent**, and CG, DK its cosineand cotangent. Make the angle BCM equal to ACF; draw the perpendicular MO; ...

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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore

### Populære avsnitt

Side 94 - 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.

Side 53 - 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 at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.

Side 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

Side 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 40 - 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 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...