The Quadrature of the Circle: The Square Root of Two, and the Right-angled TriangleWilstach, Baldwin & Company, printers, 1874 - 164 σελίδες |
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Σελίδα 35
... perpendicular be drawn from the right angle to the base the triangles on each side are sim · ilar to the whole triangle and to one another , and the perpendicular is a mean proportional between the segments of the base , and each of the ...
... perpendicular be drawn from the right angle to the base the triangles on each side are sim · ilar to the whole triangle and to one another , and the perpendicular is a mean proportional between the segments of the base , and each of the ...
Σελίδα 54
... perpendicular to ỮA , and through A ′ draw A'B ' parallel to AB . Since the new polygon is to have twice as many sides as the given polygon , the angle at its center must be one - half the angle AOB ; therefore the an- gle AO'B , which ...
... perpendicular to ỮA , and through A ′ draw A'B ' parallel to AB . Since the new polygon is to have twice as many sides as the given polygon , the angle at its center must be one - half the angle AOB ; therefore the an- gle AO'B , which ...
Σελίδα 64
... perpendicular to one another ; thus QR is perpendicular to ST and XY to ZV ; but perpendicular lines are not always vertical and horizontal ; XY is a horizontal line , and ZV is a vertical line . ANGLES . 17. If there is only one angle ...
... perpendicular to one another ; thus QR is perpendicular to ST and XY to ZV ; but perpendicular lines are not always vertical and horizontal ; XY is a horizontal line , and ZV is a vertical line . ANGLES . 17. If there is only one angle ...
Σελίδα 68
... perpendicular let fall from one extremity of the arc on the radius passing through the other extremity . Thus FG is the sine of the arc AF , or of the angle ACF . Every sine is half the chord of double the arc . Thus the sine FG is the ...
... perpendicular let fall from one extremity of the arc on the radius passing through the other extremity . Thus FG is the sine of the arc AF , or of the angle ACF . Every sine is half the chord of double the arc . Thus the sine FG is the ...
Σελίδα 74
... perpendicular of another , so that they shall touch one another in those points which contain the right angles , and also in those points which form the verticle angles , so that any two of the bases when taken together shall be equal ...
... perpendicular of another , so that they shall touch one another in those points which contain the right angles , and also in those points which form the verticle angles , so that any two of the bases when taken together shall be equal ...
Άλλες εκδόσεις - Προβολή όλων
The Quadrature of the Circle: The Square Root of Two, and the Right-Angled ... William Alexander. Myers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
The Quadrature of the Circle: The Square Root of Two, and the Right-Angled ... William Alexander Myers Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
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 geometrical geometricians give given arc given circle given polygon given radius given square 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 parabola perimeter perpendicular Plate polygon of double 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 square the circle straight line Substituting the numbers subtracted tangent theorem trigonometry true circumference true ratio truth unity variable
Δημοφιλή αποσπάσματα
Σελίδα 43 - 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 64 - 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 72 - 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 43 - 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 73 - 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 43 - 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 42 - The star that bids the shepherd fold, Now the top of heaven doth hold ; And the gilded car of day His glowing axle doth allay In the steep Atlantic stream, And the slope sun his upward beam Shoots against the dusky pole, Pacing toward the other goal Of his chamber in the east.
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 67 - 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.
Σελίδα 64 - A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles.