It is excellent practice for a beginner to copy a building in outline, (applying the preceding problems therein,) its full size; and then to enlarge or reduce it to any given scale, after which, he may draw by scale from his rough sketches, and proceed onwards till he has mastered any construction required A drawing is never completed till it is shaded, because without shadows, parts which are meant to project, may appear to recede, and therefore convey a false impression. Shading lines as thick as those in Prob. LVII. are very useful where properly applied; to do which, the light should always be allowed to enter the drawing at the upper left hand corner at an angle of 45°. To study the theory of a ray of light in this direction, will afford great advantages in practice, and this study is the more necessary, because no definite theory having hitherto been universally promulgated as a law for shading mathematical drawings, most artists have been compelled to contrive a system for themselves. The most effective process of shading drawings, is by judicious washes of color inclining to black. The color employed for this purpose by many draughtsmen, is indian ink; but the extreme difficulty of producing clear, uniform surfaces, without a tedious repetition of light tints, renders it a very disagreable shading tint to any but expert artists. The author of this work has invented an English Ink," which completely answers all the purposes of Indian ink for shading, and is so carefully prepared, that, if the student will give it only one trial, in comparison with the very best Indian ink, it is presumed he will never hereafter use the latter except for drawing lines. It may be purchased of Messrs. Rowney, Dillon, and Rowney, the author's agents, 51, Long Acre, London, (the publishers of his works on surveying, &c.,) and of all Stationers. ERRATA: In a few copies only, at 19 page, three lines from bottom, read, "AB bears the same proportion to BC, as ab does to bc." At page 25, the 4th line from bottom, read, "curved equally towards the line which bisects the angle." At page 67, seven lines from bottom, read, "equal to any side of one polygon." INDEX. N. B. Names of figures and terms not in the Index, may be Addition of plane figures Altitude or height Angles, plane, right, acute, obtuse, and spherical at centre or circumference of polygons corresponding, equal, re-entering, and salient exterior, interior in or on a segment ........ ...... Page to make, various Arcs, arches, and voussures Area, the quantity of surface Base of a figure or drawing Centre, concentric, and eccentric Chord or subtense, diameter Circle, circumference, circumscribe Complement and supplement, common ...... 11, 19, 30 17, 18 13, 39, 40, 41 18, 56-68 19, 35, 73 18, 57 12, 17, 19, 38 18, 51 12, 20, 41, 63, 67 11, 13, 14, 34 7 12, 13, 23, 26, 27, 49, 62 20, 22, 41 20, 53 16, 47, 54, 73 21, 34, 35, 71, 72 an ellipse, conjugate and transverse ...... Diagonal lines and scales Directrix, dirigent, and describent Division of lines and figures ........ Dotted, continued, and thick lines ...... ........ Elevation, plan, and section 22, 25 23, 56 19, 42 22 20, 53 Eccentric, non-concentric, and concentric Ellipse, Ellipses, oval ........ Equal, equivalent, and identical ...... Figures, rectilineal, polygonal, and similar ... .... 14, 15, 19, 20, 21, 22, 56, 65 .... 10, 11, 12, 14, 18, 19, 54 5, 6, 7, 8, 18, 55 19, 54, 67 20, 42, 43, 51 7, 21, 25, 71 Lines, straight, or right, curved, mixed, horizontal, vertical, continued, dotted, thick, and colored Mathematical calculator, Pease's Means, arithmetical, geometrical, and harmonical ...... Parallelogram, rhombus, rhomboid, rectangle .. Page 7, 8, 9, II, 17, ...... 7, 21, 36, 55, 74 21, 70 15, 16, 33, 60, 66, 67 17, 28, 29 16, 33, 55, 58, 64, 71, 72 Planes, horizontal, vertical, inclined, parallel, oblique 14, 17, 18, 19, 46-52, 58, 62 ...... Protractor, semicircular, or rectangular, to use the Quadrant, semicircle, segment, sector .... .... 7 11, 22, 24 18, 21, 22, 47, 54 19, 35-38, 54, 67, 71 13, 23, 37, 44, 45, 46, 65 ........ ...... 15, 16, 21, 33, 55, 65, 70 Scales, plain, diagonal, comparative, trigonometrical, vernier 35, 36, 73 Scalene triangles 15, 30, 56, 57 Secants, the lines A B, A O, D B, and A L, vide Probs. X, XXI, Trapezium, A B C D, in Prob. LIX. Trapezoid, A B E C, in Prob. 14, 15, 19, 29, 41, 44, 45, 54, 57–60, 61, 64, 65, 66 Trisect, and trisections 9, 10, 18, 19, 25, 44, 45 James Black, Printer, Powis Street, Woolwich. |