The Elements of Euclid: viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's DataBell & Bradfute, 1835 - 513 Seiten |
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Seite 314
... Arch . de Sph . et Cyl . and the moderns explain that term ) is the number which multiplied into the consequent term of a ra- tio produces the antecedent , or , which is the same thing , the number which arises by dividing the ...
... Arch . de Sph . et Cyl . and the moderns explain that term ) is the number which multiplied into the consequent term of a ra- tio produces the antecedent , or , which is the same thing , the number which arises by dividing the ...
Seite 461
... arch AD ; and quadrupling the con- sequents , the angle ABC will be to four right angles , as the arch AC to four times the arch AD , or to the whole circum- ference . LEMMA II . FIG . 2 . Let ABC be a plane rectilineal angle as before ...
... arch AD ; and quadrupling the con- sequents , the angle ABC will be to four right angles , as the arch AC to four times the arch AD , or to the whole circum- ference . LEMMA II . FIG . 2 . Let ABC be a plane rectilineal angle as before ...
Seite 462
... arch , of so many degrees , minutes , seconds , & c . is the angle , of which that arch is the mea- sure said to be ; thus a right angle is said to be an angle of 90 ° , because its measure , a quadrant , contains 90 ° . COR . Whatever ...
... arch , of so many degrees , minutes , seconds , & c . is the angle , of which that arch is the mea- sure said to be ; thus a right angle is said to be an angle of 90 ° , because its measure , a quadrant , contains 90 ° . COR . Whatever ...
Seite 463
... arch AC or of the angle ABC , of which AC is the measure . COR . 1. The sine of a quadrant , or of a right angle , is equal to the radius . COR . 2. The sine of any arch is half the chord of double that arch ; for the diameter which ...
... arch AC or of the angle ABC , of which AC is the measure . COR . 1. The sine of a quadrant , or of a right angle , is equal to the radius . COR . 2. The sine of any arch is half the chord of double that arch ; for the diameter which ...
Seite 464
... arch and a quad- rant is called the complement of that arch . Thus HC is the complement of the arch AC , or of the arch FC . X. Let HK be the tangent , CL or DB , which is equal to it , the sine , and BK the secant of CBH , the ...
... arch and a quad- rant is called the complement of that arch . Thus HC is the complement of the arch AC , or of the arch FC . X. Let HK be the tangent , CL or DB , which is equal to it , the sine , and BK the secant of CBH , the ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Keine Leseprobe verfügbar - 2019 |
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ABCD altitude angle ABC angle BAC arch base BC BC is equal BC is given bisected Book XI centre circle ABC circumference cone cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore
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Seite 95 - 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.
Seite 153 - 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.
Seite 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Seite 11 - 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.
Seite 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Seite 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Seite 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Seite 26 - 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.
Seite 11 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 93 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. VII. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.