Page:Philosophical Transactions - Volume 003.djvu/251

 Spherical Trigonometry. Those that desire to be farther satisfied, may read Trigonometria Britannica of Gellibrand and Newton, the Idea Trigonometriæ by the Lord Bishop of Sarum, Dr. Seth Ward; and also Bonavent. Cavalerii Trigonometria, and his Directorium Universale Uranometricum, but especially his Compendio delle Regole Trigonometriche & Centuria di Problemi.

2. Of Practical Geometry 3 Books.

In the First the Author handleth

The Construction of the Tables of Sines, Tangents, and Secants.

The Resolution of Right-lined Triangles.

The Mensuration of the distance of Objects, as well unaccessible as accessible.

The Heights of Mountains, Towers, Clouds, Rainbowes, the Depths of Wells and Vallies. He concludes the perpendicular height of the burning Mountain Ætna to exceed 5 Bononian Miles; of Mount Caucasus beyond the Caspian-Sea to be 51. Mount Athos of Greece 28. Casius of Syria 20. the Alpes of Italy and Pic of Tenariffe 10 Miles The Circumference of the Earth, the Distances of the Sun, Moon, and Earth.

In the second Book, he handles the Dimension of Plain Surfaces, either Regular or Irregular, and takes the Ichnography or Description in Paper, of any Figure given of the surface of the Earth: Asserts the Possibility of the Quadrature of the Circle, and handles the Transformation of Plain Figures, to wit, their Addition, Subtraction, Augmentation, Diminution, Comparison; further the dividing of a Plain Triangle, in a given Reason by a line passing through a Point any where assigned: This he doth largely in 16 Propositions, because upon it chiefly depends the Division of other Right-line Figures; and because he found divers Determinations wanting, when the point is given within. Those that are desirous to see this Analytically done, may find it in Herigon with a Construction thereof; as also a Geometrick Construction thereof in Van Schootens Miscellanea; and another most excellent Construction at the end of Van Ceulen de Circulo & Adscriptis.

Afterwards our Author proceeds to the dividing of other Figures, in a given Reason, or by parallel lines, and sheweth how to apply the whole to Practice in the Field.

In the third Book the Author first measureth such Solids as are contained under a Plain Surface. Secondly, such as are contained under a Curved Surface. Thirdly, He measureth the Mundane Bodies, as the Surface of the whole Earth; where he is pleased to conclude, that at the Day of Judgement, a less portion of it then England, will serve to hold all its Inhabitants, and their Infants, that ever have been, or in likelihood may be hereafter, till then, supposing the World should last 10000 years. He measureth also the Solidity of the Earth, and Ocean; the Magnitude of the Sun, Moon, Rh