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 Spherical TrignonometryBell & Bradfute, 1875 - 257 pagine |
Dall'interno del libro
Risultati 1-5 di 15
Pagina 168
... cosine of the arc or of the angle . VI . A straight line touching the circle at one extremity of the arc , and extending to the diameter which passes through the other extremity , is called the tangent of the arc or of the angle . VII ...
... cosine of the arc or of the angle . VI . A straight line touching the circle at one extremity of the arc , and extending to the diameter which passes through the other extremity , is called the tangent of the arc or of the angle . VII ...
Pagina 169
... cosine ; AE its tangent ; BE its secant ; AD its versed sine ; HK its cotangent ; BK its cosecant . F I H D K E 5. COR . 1. The sine of a quadrant ( a quarter of the circum- ference ) , or of a right angle , is equal to the radius ; and ...
... cosine ; AE its tangent ; BE its secant ; AD its versed sine ; HK its cotangent ; BK its cosecant . F I H D K E 5. COR . 1. The sine of a quadrant ( a quarter of the circum- ference ) , or of a right angle , is equal to the radius ; and ...
Pagina 170
... cosine ) of the sum or difference is the same ( abstracting from sign ) as that of the angle itself ; but if an angle be added to , or taken from one right angle , the function of the sum or difference is the comple- mentary function of ...
... cosine ) of the sum or difference is the same ( abstracting from sign ) as that of the angle itself ; but if an angle be added to , or taken from one right angle , the function of the sum or difference is the comple- mentary function of ...
Pagina 173
... cosine , and tangent of 60 ° and 30. ° C Let ABC be an equilateral triangle ; AB = 1 . Draw CD per- pendicular to the base AB ; then it bisects AB ( 1. 26 ) . Hence cos 60 ° = cos ABC = BD = 1BA = 1 , and BD + CD2 - CB2 = 1 ( I. 47 ) ...
... cosine , and tangent of 60 ° and 30. ° C Let ABC be an equilateral triangle ; AB = 1 . Draw CD per- pendicular to the base AB ; then it bisects AB ( 1. 26 ) . Hence cos 60 ° = cos ABC = BD = 1BA = 1 , and BD + CD2 - CB2 = 1 ( I. 47 ) ...
Pagina 174
... cosine is positive , and in the nearer , negative . Having thus determined the sign of the sine and the cosine , the relations exhibited in Art . 10 , enable us to determine the signs of the other trigonometrical functions . For , since ...
... cosine is positive , and in the nearer , negative . Having thus determined the sign of the sine and the cosine , the relations exhibited in Art . 10 , enable us to determine the signs of the other trigonometrical functions . For , since ...
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Elements of Geometry; Containing the First Six Books of Euclid, With Two ... John 1748-1819 Playfair Anteprima non disponibile - 2021 |
Parole e frasi comuni
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore given circle given point given straight line hypotenuse inscribed less Let ABC Let the straight meet multiple opposite angle parallel parallelogram perpendicular plane polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles segment semicircle similar sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC straight line drawn tangent THEOR third three straight lines touches the circle triangle ABC triangle DEF wherefore