The Quadrature of the Circle: The Square Root of Two, and the Right-angled TriangleWilstach, Baldwin & Company, printers, 1873 - 164 páginas |
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Página 46
... hence , the whole perimeter of this polygon must be six times the radius of the circle , or three times the diameter . The chord bd is bisected by CA. Produce Cb and Cd , and through the point A , draw BD parallel to bd ; BD will then ...
... hence , the whole perimeter of this polygon must be six times the radius of the circle , or three times the diameter . The chord bd is bisected by CA. Produce Cb and Cd , and through the point A , draw BD parallel to bd ; BD will then ...
Página 47
... whence CM : MK :: CA : AD CM . AD = СА . МК But from equation ( 3 ) we see that each member of this last equation is equal to 2x ; hence equation 4 becomes 2x . 2x ab = If we multiply both members of this by n2 = INTRODUCTION . 47.
... whence CM : MK :: CA : AD CM . AD = СА . МК But from equation ( 3 ) we see that each member of this last equation is equal to 2x ; hence equation 4 becomes 2x . 2x ab = If we multiply both members of this by n2 = INTRODUCTION . 47.
Página 48
... hence , AE : AEED :: CM : CM + CA. Multiplying the first couplet of this proportion by CA , and the second by MK , observing that AE + ED = AD , we shall have = = AE.CA : AD.CA :: CM.MK : ( CM + CA ) MK . But AE.CA measures the area of ...
... hence , AE : AEED :: CM : CM + CA. Multiplying the first couplet of this proportion by CA , and the second by MK , observing that AE + ED = AD , we shall have = = AE.CA : AD.CA :: CM.MK : ( CM + CA ) MK . But AE.CA measures the area of ...
Página 50
... hence , they are proportional to the polygons themselves . But CAM is a mean proportional between CAD and CEM ( B. IV . , P. XXIV . , C. 2 ) ; consequently p ' is a mean proportional between p and P : hence , p ' ′ = √ p × P. . . . ( 1 ...
... hence , they are proportional to the polygons themselves . But CAM is a mean proportional between CAD and CEM ( B. IV . , P. XXIV . , C. 2 ) ; consequently p ' is a mean proportional between p and P : hence , p ' ′ = √ p × P. . . . ( 1 ...
Página 51
... hence ( B. II . , P. II . ) , CPM : CPE :: CD : CA or CM . But , the triangles CAD and CAM have the common altitude AD ; they are therefore , to each other as their bases : hence , CAD : CAM :: CD : CM ; or , because CAD and CAM are to ...
... hence ( B. II . , P. II . ) , CPM : CPE :: CD : CA or CM . But , the triangles CAD and CAM have the common altitude AD ; they are therefore , to each other as their bases : hence , CAD : CAM :: CD : CM ; or , because CAD and CAM are to ...
Otras ediciones - Ver todas
The Quadrature of the Circle the Square Root of Two and the Right-Angled ... William Alexander Myers Vista previa limitada - 2023 |
The Quadrature of the Circle the Square Root of Two and the Right-Angled ... William Alexander Myers Vista previa limitada - 2023 |
The Quadrature of the Circle, the Square Root of Two, and the Right-Angled ... William Alexander. Myers Sin vista previa disponible - 2013 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 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...
Página 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...
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.