Proposition 1 of the book On Sizes states that two equal spheres ...

Proposition 1 of the book On Sizes states that two equal spheres are comprehended by one and the same cylinder, and two unequal spheres by one and the same cone which has its vertex in the direction of the lesser sphere; and the straight line dra

Proposition 2 of the book On Sizes states that if a sphere ...

Proposition 2 of the book On Sizes states that if a sphere be illuminated by a sphere greater than itself, the illuminated portion of the former sphere will be greater than a hemisphere (Heath 1913:358).

Proposition 3 of the book On Sizes states that the circle in ...

Proposition 3 of the book On Sizes states that the circle in the moon which divides the dark and the bright portions is least when the cone comprehending both the sun and the moon has its vertex at our eye (Heath 1913:362).

Proposition 4 of the book On Sizes states that the circle CD ...

Proposition 4 of the book On Sizes states that the circle CD which divides the seen and the unseen portions of the moon is not perceptibly different from a parallel great circle EF on the moon (Heath 1913:365).

Proposition 6 of the book On Sizes states that the moon moves ...

Proposition 6 of the book On Sizes states that the moon moves [in an orbit] lower than [that of] the sun, and, when it is halved, is distant less than a quadrant from the sun (Heath 1913:372).

Proposition 7 of the book On Sizes states that the distance of ...

Proposition 7 of the book On Sizes states that the distance of the sun from the earth is greater than 18 times, but less than 20 times, the distance of the moon from the earth (Heath 1913:377). In other words, the sun is 18 to 20 times farther aw

Proposition 13 of the book On Sizes states that the straight line ...

Proposition 13 of the book On Sizes states that the straight line subtending the portion intercepted within the earth's shadow of the circumference of the circle in which the extremities of the diameter of the circle dividing the seen and the uns

Proposition 14 of the book On Sizes states that the straight line ...

Proposition 14 of the book On Sizes states that the straight line joined from the centre of the earth to the centre of the moon has to the straight line cut off from the axis towards the centre of the moon by the straight line subtending the [cir

Proposition 15 of the book On Sizes states that the diameter of ...

Proposition 15 of the book On Sizes states that the diameter of the sun has to the diameter of the earth a ratio greater than 19/3, but less than 43/6 (Heath 1913:403). This means that the sun is (a mean of) 6_ times wider than earth, or that the

Proposition 17a in al-Tusi's medieval Arabic version of the book On Sizes ...

Proposition 17a in al-Tusi's medieval Arabic version of the book On Sizes states that the ratio of the distance of the vertex of the shadow cone from the center of the moon (when the moon is on the axis of the cone containing the earth and the su

No restrictions on your remixing, redistributing, or making derivative works. Give credit to the author, as required.

Your remixing, redistributing, or making derivatives works comes with some restrictions, including how it is shared.

Your redistributing comes with some restrictions. Do not remix or make derivative works.

Copyrighted materials, available under Fair Use and the TEACH Act for US-based educators, or other custom arrangements. Go to the resource provider to see their individual restrictions.