The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 sider |
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Side 464
... cosine , and BK the cosecant of the angle ABC . COR . 1. The radius is a mean proportional between the tan- gent and cotangent of any angle ABC . For , since HK , BA are parallel , the angles HKB , ABC are equal , and KHB , BAE are ...
... cosine , and BK the cosecant of the angle ABC . COR . 1. The radius is a mean proportional between the tan- gent and cotangent of any angle ABC . For , since HK , BA are parallel , the angles HKB , ABC are equal , and KHB , BAE are ...
Side 465
... cosine , cot for cotan- gent , cosec for cosecant ; and sin2 , cos2 , tan2 , rad2 , & c . for the squares of the sine , cosine , tangent , radius , & c . re- spectively . NOTE 2. In a right angled triangle , the side subtending the ...
... cosine , cot for cotan- gent , cosec for cosecant ; and sin2 , cos2 , tan2 , rad2 , & c . for the squares of the sine , cosine , tangent , radius , & c . re- spectively . NOTE 2. In a right angled triangle , the side subtending the ...
Side 468
... cosine of half the difference of any two angles is to the cosine of half their sum , as the sum of the opposite sides to the third side ; and the sine of half the difference of any two angles is to the sine of half their sum , as the ...
... cosine of half the difference of any two angles is to the cosine of half their sum , as the sum of the opposite sides to the third side ; and the sine of half the difference of any two angles is to the sine of half their sum , as the ...
Side 469
... cosine of the angle included by the two sides . Let ABC be a plane triangle , twice the rectangle contained by AB , BC , is to the difference between the sum of the squares of AB , BC , and the square of the base AC , as the radius to ...
... cosine of the angle included by the two sides . Let ABC be a plane triangle , twice the rectangle contained by AB , BC , is to the difference between the sum of the squares of AB , BC , and the square of the base AC , as the radius to ...
Side 471
... cosine of half the contained angle . In the plane triangle ABC , if the perimeter be denoted by P , then will AB.AC : P ( P - BC ) :: rad : cos BAC . For , the same construction being made as in the preceding proposition , in the right ...
... cosine of half the contained angle . In the plane triangle ABC , if the perimeter be denoted by P , then will AB.AC : P ( P - BC ) :: rad : cos BAC . For , the same construction being made as in the preceding proposition , in the right ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Ingen forhåndsvisning - 2019 |
Almindelige termer og sætninger
ABC is given altitude angle ABC angle BAC arch base BC BC is equal bisected Book XI centre circle ABCD 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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Side 47 - 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, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.
Side 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.
Side 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- 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.
Side 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...
Side 170 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Side 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.
Side 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Side 28 - 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 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.
Side 5 - 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...