The Quadrature of the Circle: The Square Root of Two, and the Right-angled TriangleWilstach, Baldwin & Company, printers, 1873 - 164 σελίδες |
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Σελίδα 8
... sine No. 1 was divided into 14 parts , and each part was 76 . COINCIDENCE FROM HOLY WRIT . See Genesis , Exodus , Leviticus , Numbers , and St. Matthew for the number 14 . See Genesis and Daniel for the number 70 . By Case 2 , the ...
... sine No. 1 was divided into 14 parts , and each part was 76 . COINCIDENCE FROM HOLY WRIT . See Genesis , Exodus , Leviticus , Numbers , and St. Matthew for the number 14 . See Genesis and Daniel for the number 70 . By Case 2 , the ...
Σελίδα 35
... sine as the radius is to the tangent , consequently the secant is to the tangent as the radius is to the sine , therefore the square of the secant is to the square of the tangent as the square of the radius is to the square of the sine ...
... sine as the radius is to the tangent , consequently the secant is to the tangent as the radius is to the sine , therefore the square of the secant is to the square of the tangent as the square of the radius is to the square of the sine ...
Σελίδα 38
... sine = , is not quite the part of the true circumference though very near it , being the chord of double the arc , whose sine is . If then we assume to be the true diameter , and 44 to be the true circumference , and they are very near ...
... sine = , is not quite the part of the true circumference though very near it , being the chord of double the arc , whose sine is . If then we assume to be the true diameter , and 44 to be the true circumference , and they are very near ...
Σελίδα 43
... the quadrature of the circle , 1st . That the cosine must always intercept the sine at right angles , and the radius must always intercept the tangent at right angles . 2d . The tangent is always greater than the arc INTRODUCTION . 43.
... the quadrature of the circle , 1st . That the cosine must always intercept the sine at right angles , and the radius must always intercept the tangent at right angles . 2d . The tangent is always greater than the arc INTRODUCTION . 43.
Σελίδα 44
... sine is always less than the arc to which it belongs , for the tangent lies wholly without the circle while the sine lies wholly within the circle , and the arc to which they belong must lie between them ; therefore , as far as the sine ...
... sine is always less than the arc to which it belongs , for the tangent lies wholly without the circle while the sine lies wholly within the circle , and the arc to which they belong must lie between them ; therefore , as far as the sine ...
Άλλες εκδόσεις - Προβολή όλων
The Quadrature of the Circle the Square Root of Two and the Right-Angled ... William Alexander Myers Περιορισμένη προεπισκόπηση - 2023 |
The Quadrature of the Circle the Square Root of Two and the Right-Angled ... William Alexander Myers Περιορισμένη προεπισκόπηση - 2023 |
The Quadrature of the Circle, the Square Root of Two, and the Right-Angled ... William Alexander. Myers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
apothem arc cutting Archimedes ARTICLE assumed circumference assumed diameter Bisect chord circumscribed double triangle circumscribed polygon consequently cosine cumference curve decimal places deducted demonstration diagonal difference discovery division and cancellation double the number draw expressed extracting the square figures geometricians geometry give given arc given circle given polygon given radius given triangle half the number hyperbola hypothenuse hypothesis infinite inscribed and circumscribed inscribed double triangle inscribed polygon inscribed square James Gregory less limit mathematical mean proportional method multiplied number of sides Oronce Finée parabola perimeter perpendicular Plate polygon of double Polygons are Carried problem PROPOSITION quadrature quantity radius rectangle contained regular polygon result already established right angle right line right-angled triangle Scholium secant sine solution square described square root straight line subtracted tangent theorem triangle DAC trigonometry true circumference true ratio truth unity variable
Δημοφιλή αποσπάσματα
Σελίδα 65 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Σελίδα 39 - It furnishes art with all her materials, and without it judgment itself can at best but " steal wisely : " for art is only like a prudent steward that lives on managing the riches of nature.' Whatever praises may be given to works of judgment, there is not even a single beauty in them to which the invention...
Σελίδα 71 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal.
Σελίδα 39 - Nor is it a wonder if he has ever been acknowledged the greatest of poets, who most excelled in that which is the very foundation of poetry. It is the invention that in different degrees...
Σελίδα 78 - COR. From this it is manifest, that the perpendicular drawn from the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base; and also that each of the sides is a mean proportional between the base, and...
Σελίδα 71 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Σελίδα 39 - And perhaps the reason why common critics are inclined to prefer a judicious and methodical genius to a great and fruitful one, is, because they find it easier for themselves to pursue their observations through an uniform and bounded walk of art, than to comprehend the vast and various extent of nature.
Σελίδα 31 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Σελίδα 74 - In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the sum of the squares described on the sides which contain the right angle.
Σελίδα 69 - The circumference of every circle is supposed to be divided into 360 equal parts, • called degrees, each degree into 60 minutes, and each minute into 60 seconds, etc.