C ο Ν Τ Ε Ν Τ S. Τ PAGE GEometrica! Definitions and Problems Practical Questions in Trigonometry, &c. Areas of Right-Lined and Circular Figures Practical Questions concerning Areas Mensuration of Solids, General Definitions Of Prisms, Pyramids, and the Sphere, &c. Of Conic Sections, and their Solids Of the Ellipse, and Figures generated by it Parabolic Lines, Areas, Surfaces and Solidities Hyperbolic Lines, Areas, Surfaces, and Solidities Practical Questions concerning Solids The true Quadrature and Cubature of Figures Method of Equidistant Ordinates and Sections The Mensuration of Figures, by the Center of Gravity Description and Use of the Instruments Practical Questions in Surveying Description and Use of the Instruments Of Caiks, as divided into several Varieties Of gauging Calks by their Mean Diameters To gauge any Caik by Four Dimensions To gauge any Cask by Three Dimensions only À : ON Μ Ε Ν S Ο R Α Τ Ι Ο Ν. 1. A POINT has no parts nor dimensions, neither length, breadth, nor thickness. 2. A line is length, without breadth or thickness. 3. A surface, or superficies, is an extension, or a figure, of two dimensions, length and breadth ; but without thickness. 4. A body or solid, is a figure of three dimensions, namely, length, breadth, and thickness. Hence surfaces are the extremities of solids; lines the extremities of surfaces; and points the extremities of lines. 5. Lines are either right, or curved, or mixed of these two. 6. A right line, or straight line, lies all in the same direction, between its extremities; and is the shortest distance between two points. 7. A curve continually changes its direction, between its extreme points. 8. Lines are either parallel, oblique, perpendicular, or tangential. 9. Parallel lines are always at the same distance; and never meet, though ever so far produced. 10. Oblique right lines change their distance, and would meet, if produced, on the side of the least distance. 11. One line is perpendicular to another, when it inclines not more on the one side than on the other. 12. One line is tangential, or a tangent to another, when it touches it, without cutting, when both are produced. 13. An angle is the inclination, or opening, of two lines, having different directions, and meeting in a point. 14. Angles are right or oblique, acute or obtuse. 15. A right angle, is that which is made by one line perpendicular to another. Or when the angles on each fide are equal to one another, they are right angles. 16 An oblique angle is that which is made by two oblique lines; and is either less or greater than a right angle. 17. An acute angle is less than a right angle. 18 An obtuse angle is greater than a right angle. 19. Superficies are either plane or curved. 20. A plane, or plane superficies, is that with which a right line may, every way, coincide. But if not, it is curved. 21. Plane figures are bounded either by right lines or curves. 22. Plane figures bounded by right lines, have names according to the number of their fides, or of their angles; for they have as many sides as angles; the least number being three. 23. A figure of three sides and angles, is called a triangle. And it receives particular denominations from the relations of its sides and angles. 24. An equilateral triangle, is that whose three sides are all equal. 25. An isosceles triangle, is that which has two sides equal. 26. A scalene triangle, is that whose three sides are all unequal. 27. A right-angled triangle, is that which has one right angle. 28. Other triangles are obliqueangled, and are either obtuse or acute. 29. An obtuse-angled triangle has one obtuse angle. 30. An acute-angled triangle has all its three angles acute. 31. A figure of four sides and angles, is called a quadrangle, or a quadrilateral. 32. A parallelogram is a quadrilateral which has both its pairs of opposite sides parallel. And it takes the following particular names. 33. A rectangle is a parallelogram, having all its angles right ones. 34. A square is an equilateral rectangle; having all its fides equal, and all its angles right ones. 35. A rhomboid is an obliqueangled parallelogram. 36. A rhombus is an equilateral rhomboid; having all its sides equal, but its angles oblique. 37. A trapezium is a quadrilateral which has not both its pairs of opposite fides parallel. 38. A trapezoid has only one pair of opposite fides.parallel. 39. A diagonal is a right line joining any two opposite angles of a quadrlateral. |