## The Quadrature of the Circle: The Square Root of Two, and the Right-angled Triangle |

### From inside the book

Page 67

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**circle is supposed to be divided into 360 equal parts , called degrees ; each degree into 60**minutes , and each min- ute into 60 seconds . Degrees , minutes , and seconds are designated by the characters " . Thus 23 ° 14 ′ 35 ′′ is read ...### Other editions - View all

The Quadrature of the Circle, the Square Root of Two, and the Right-Angled ... William Alexander. Myers No preview available - 2013 |

### Common terms and phrases

apothem arc cutting arc DF Archimedes ARTICLE assumed circumference assumed diameter Bisect chord circumscribed double triangle circumscribed polygon consequently cosine cumference curve decimal places deducted demonstration diagonal difference discovery divided division and cancellation double the number draw expressed extracting the square FIGURE geometricians geometry give given arc given circle given polygon given radius given triangle hyperbola hypothenuse 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 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 triangle DAC trigonometry true circumference true ratio truth unity variable

### Popular passages

Page 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.

Page 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...

Page 68 - 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.

Page 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...

Page 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...

Page 69 - 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...

Page 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.

Page 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.

Page 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.

Page 64 - 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.