ER PB Reto MATHEMATICS. 
(The numbers refer to the top paging of the text.] 
ALGEBRA, application of, to geometry, 23 ; alge- 
braic curves, 24. 
Angles, definitions of, 2; alternate and opposite 
angles, 4 
Area of a rectilineal figure, to determine the, 32. 
Areas, of the equivalence of, in figures, 8 ; 
problems solved by, 9. 
Astrolabe, the, 62. 
Borda’s reflecting circle, 67. 
Cardioid, the, 26. 
Circle, subdivisions of, 3 ; general properties and 
measurement of, 10 ; construction of polygons 
in and about, 11; lines allied to the, 12; 
repeating and compensating, 65 ; the levelling, 
Cissoid, the, 25. 
Compass, the, 63 ; the prismatic, 64 ; levelling, 70. 
Compasses, hair, bisecting, proportional, beam, 
triangular, and plate, 53-55; eccentric, 56 ; 
spring, 57 ; erecting, 60. 
Conchoid, the, 25. 
Cone, the, 16. 
Conic sections, the, 24; proierson of the three 
principal, 37. 
Cosine, explanation of, 18. 
Co-tangent, explanation of, 18. 
Curves, divisions of, 24; various algebraic, 25; 
transcendental, 26; projection of curved lines, 
35; curved surfaces of elevation, 44. 
Cycloid, the, 26. 
Cylinder, the, 15. 
Diopter, or sight ruler, 60. 
Eidograph, the, 57. 
Ellipse, the, 24. 
Elliptographs, 55. 
Evolutes, 27. 
Farey’s elliptograph, 55. 
Figure, definition of, 2; description of the prin- 
cipal figures, 3 ; equality of figures, 5; simi- 
larity of, 7; when said to be equivalent, 8 ; 
the square a unit of measure of the superficial 
relations of, 9; method of determining the 
area of a rectilineal, 32. 
Geodesy, application of trigonometry to, 22; 
geodesy or surveying, 28. 
Geometry, definition of, and subdivisions, 1 ; 
geometry of solids, 13; of curves, 23; analy- 
tical, ib. ; ; definition of practical, 28 ; descrip- 
tive, 34. 
Graphometer, the, 66. 
Gunter's chain, 58. 
Hadley, the inventor of reflecting instruments, 
66 ; his sextant, ib. 
Higher geometry, 23. 
Hyperbola, the, 25. 
Involutes, 27. 
Lehman, his method of topographical drawing, 
33 ; modifies the plane table, 59. 
Lemniseata, the, 26. 
Level, the, 60 ; foot, water, and mercurial, 68 ; 
and compass, 69. 
Levelling, 28, 33 ; instruments, 68. 
Lines, different kinds of, 2; position of straight 
lines in the same plane, 4; position of, in 
space, 13 ; spiral, 26. 
Magnitude, definition of, 1 ; three different kinds 
of, ib. 
Mason’s level, the, 68. 
Mathematical and surveying Srateniniatites de- 
scription of, 53. 
Mathematics, definition of, and subdivisions, 1. 
Mayer's plane table, 59. 
Measuring staff, the, 58; chain, ib. 
Ophiuroid, the, 26. 
Oval, the, and the ovate, 12. 
Pantograph, the, 56. 
Parabola, the, 25. 
Parallel ruler, 57. 
Parallelograms, four different kinds of, 3. 
Perspective, linear, mathematical principles of, 50. 
Plans table, the, 59. 
Planes, position of, in space, 13; vertical and 
horizontal, 34; plane surfaces, shades and 
shadows on, 44. 
Planimetry, or Plane Geometry, 2; 
definitions, ib. 
Polygons, 3; construction of, in and about a 
circle, 11. 
Prisms, 14. 
Projection, theory of, 34; in vertical and hori- 
zontal planes, ib. ; projection of shadows, 43 ; 
of shades and shadows upon plane surfaces 
and curved surfaces of elevation, 44; on hol- 
low, straight, and curved surfaces, 48. 
Protractor, the, 58. 
Pyramids, 15. 
general 
Quadrangles, or quadrilateral figures, 3; con- 
struction of various, 6. 
Quadratrix, the, 27. 
Reflecting instruments. 66; reflecting circle of 
Borda, 67. 
Reticulation of bodies, 41. 
Round bodies, 15. 
Scheinur's pantograph, 56. 
Schms:kalder’s prismatic compass, 64. 
