Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids. To which are Added, Elements of Plane and Sperical TrigonometryW.E. Dean, 1844 - 317 sider |
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Side 219
... sine of a quadrant , or of a right angle , is equal to the radius . COR . 2. The sine of an arc is half the chord of twice that arc : this is evi- dent by producing the sine of any arc till it cut the circumference . H K L T D 5. The ...
... sine of a quadrant , or of a right angle , is equal to the radius . COR . 2. The sine of an arc is half the chord of twice that arc : this is evi- dent by producing the sine of any arc till it cut the circumference . H K L T D 5. The ...
Side 220
... sine , tangent , or secant of the complement of any angle is called the Cosine , Cotangent , or Cosecant of that angle . Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant of ...
... sine , tangent , or secant of the complement of any angle is called the Cosine , Cotangent , or Cosecant of that angle . Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant of ...
Side 221
... sine of the angle C , ( Def . 4. ) ; therefore CB : BAR sin . C. Also , because EG touches the cir- cle in E , CEG is a right angle , and therefore equal to the angle BAC ; and since the angle at C is common IB G D FE to the triangles ...
... sine of the angle C , ( Def . 4. ) ; therefore CB : BAR sin . C. Also , because EG touches the cir- cle in E , CEG is a right angle , and therefore equal to the angle BAC ; and since the angle at C is common IB G D FE to the triangles ...
Side 222
... sin . B ; and for the same reason , AC AD :: R : sin . C , and inversely , AD AC sin . CR ; therefore , ex æquo ... sine of AB , DK is the sum of the sines of the arcs AC and AB , and CK is the difference of their sines ; DAB also ...
... sin . B ; and for the same reason , AC AD :: R : sin . C , and inversely , AD AC sin . CR ; therefore , ex æquo ... sine of AB , DK is the sum of the sines of the arcs AC and AB , and CK is the difference of their sines ; DAB also ...
Side 226
... sine of half the angle included between the two sides of the triangle . Let ABC be a triangle of which BC is the base , and AB the greater of the two sides ; 4AB.AC : ( BC + ( AB - AC ) ) × ( BC- ( AB - AC ) ) :: Ra : ( sin . BAC ) 2 ...
... sine of half the angle included between the two sides of the triangle . Let ABC be a triangle of which BC is the base , and AB the greater of the two sides ; 4AB.AC : ( BC + ( AB - AC ) ) × ( BC- ( AB - AC ) ) :: Ra : ( sin . BAC ) 2 ...
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Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1847 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1839 |
Vanlige uttrykk og setninger
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Populære avsnitt
Side 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. either the sides adjacent to the equal...
Side 68 - THE angles in the same segment of a circle are equal to one another...
Side 23 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Side 74 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 78 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 9 - 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.
Side 75 - If a straight line touch a circle, and from the point of contact a...
Side 18 - AT a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Side 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 136 - AB is (7. 5.) to AD, as AE to AG ; and DC to CB, as GF to FE; and also CD to DA, as FG to GA ; therefore the sides of the parallelograms ABCD, AEFG about the equal angles are proportionals; and they are therefore similar to one another (1.