Karl Friedrich Gauss was a German mathematician. He was born in 1777 at Brunswick and died in 1855. He demonstrated that a circle can be divided into 17 equal arcs by elementary geometry.
And in addition to many new theorems, he published a demonstration of the theorem of Fermat concerning triangular numbers. He also calculated, by a new method, the orbit of the planets Ceres and Pallas. In 1807 he became professor of mathematics and director ob the observatory of Gottingen, a position which he held until his death. Research Karl Gauss
An angle is the point where two lines meet, or the meeting of two lines in a point. A plane rectilineal angle is formed by two straight lines which meet one another, but are not in the same straight line; it may be considered the degree of opening or divergence of the two straight lines which thus meet one another.
A right angle is an angle formed by a straight line falling on another perpendicularly, or an angle which is measured by an arc of 90 degrees.
An acute angle is that which is less than a right angle.
An obtuse angle is that which is greater than a right angle.
Acute and obtuse angles are both called oblique, in opposition to right angles. Exterior or external angles are the angles of any rectilineal figure without it, made by producing the sides. A solid angle is that which is made by more than two plane angles meeting in one point and not lying in the same plane, as the angle of a cube. A spherical angle is an angle on the surface of a sphere, contained between the arcs of two great circles which intersect each other.
The replacement for Draw Applause, Applause II by Ashton Tate is a business graphics, charting, drawing, and presentation package all in one. It can be used to create slides, do on screen presentations, or create annotated charts. The picture Window includes drawing tools such as text, lines, circles, arcs, boxes, and polygons which can be used to annotate charts or create freehand illustrations. Images can be copied, moved deleted, rotated, sized, and stretched. Objects can be customised with fill colours, patterns, and line widths.
A small clip-art library of images is also available. The images are object-oriented so you can edit the individual elements. The program includes some interesting and artistic special effects. For example, you can create colour blends by picking two colours and the starting points for each in an enclosed area. The product automatically fills the colours so they blend into the centre of the object you are filling. This creates the illusion of three-dimensional objects. You can create slide shows with Applause II although there is no runtime slide show utility. Links can be established between Applause II and any data file, including Lotus 1-2-3, dBase, any Master product, or Framework. This means that presentations can be created more easily and efficiently than if you needed to key data in from scratch. Research Applause II
AutoSketch is software for drawing. As easy to use as painting software, it includes many CAD features. However, unlike typical painting software, AutoSketch keeps track of objects. This means that shapes do not get lost in a sea of dots. When an object is manipulated, it maintains its integrity as a complete unit. The product was designed for users with less demanding drawing requirements such as office layouts, simple technical drawings, and flowcharts.
AutoSketch is the best starting point for individuals who may be interested in upgrading to AutoCAD later. In addition, AutoCAD users may find AutoSketch useful in the early drawing stages.
AutoSketch can draw lines, arcs, circles, points, polygons and spline curves (free-form shapes). All basic drawing shapes can be moved, copied, stretched, rotated, mirrored, or scaled. For example, by pointing and clicking, you can create an office layout where walls and furniture can be moved or adjusted on-screen.
AutoSketch uses a mouse with pull-down menus and dialog boxes. AutoSketch includes other CAD features such as dimensioning and measuring, snap and ortho alignment, layers, and line types. Text can be added at any point, at any angle, and can be any height or width.
AutoSketch also allows you to insert another AutoSketch drawing, so you can create a library of objects for future use. Research AutoSketch
Canvas is a precision drawingpackage for the Mac that lets you create presentation materials, desktop publishing images, or architectural renderings. Its large selection of powerful, easy-to-use tools makes it one of the more popular drawing programs. Icons and menu options provide continuous multipoint Bezier curves, instant autotrace conversion of bitmap images to unlimited drawing layers, 1/65,000th of an inch precision, and text and graphics in 16.7 million colours plus PostScript grey scales in 1% increments.
For touching up clipped or scanned art, Canvas provides a number of painting tools which can be used on the same layers as the drawing tools. Canvas supports 24-bit colour on the Macintosh II, hairlines to 1/1000th of an inch, auto-dimensioning of lines and arcs, and a zoom capacity ranging from 3% to 3,200%. The program adds area and perimeter calculations, a peel-away ruler, PixelPaintcompatible colour palettes, smooth multipoint polygons, and special effects such as object rotation in one degree increments, distortion, and one or two point perspective.
Canvas also features object libraries (macros) that function as extensions to the drawing toolbox. Up to 32 objects can be added to any macro library, and macro libraries can be saved as individual files. A desk accessory version of Canvas can be invoked while working with other programs and provides approximately 80%, of the program's capabilities. The program also has a bitmap conversion option for transforming scanned colour or grey scale images into one of 15 predefined halftone or dithered images (for the Macintosh II only). Research Canvas
DrafixCAD Ultra by Foresight Resources, proves that high-quality computer-aided design and drafting do not have to cost a lot. This product includes features that you would expect to find only in much more expensive packages. DrafixCAD Ultra lets you create and manipulate a range of items including lines, arcs, ellipses, and polygons. Each item can possess numerous attributes that can be selected or changed at any time. Lines and arcs can be trimmed, divided, or stretched. Intersections can be rounded or bevelled. Symbols can be created, nested, and broken into their individual items. DrafixCAD Ultra allows you to copy, move, rotate, or scale an element, or mirror it about any axis. Elements may be designated by item, group, or region. Research DrafixCAD Ultra
Graduation is the art of dividing into the necessary spaces the scales of mathematical, astronomical, and other philosophical instruments. Common graduation is simply effected by copying from a scale prepared by a higher process; original graduation is chiefly performed either by stepping or bisection. Stepping consists in ascertaining by repeated trial with finely-pointed spring-dividers - which are made, as it were, to proceed by successive steps - the size of the divisions required, their number being known, and then finally marking them.
In bisection the beam compasses are used, an arc with a radius of nearly half the line being described from either end of the line, and the short distance between the arcs bisected with the aid of a magnifier and a fine pointer. The process is repeated, for each of the two halves thus obtained, until by subdivision the required graduation is obtained.
Ordinary instruments are graduated by machines, most of which are based upon the principle of that invented by Ramsden in 1766. In this there is a horizontal wheel, turning on a vertical axis, with a toothed edge which is advanced a certain amount (e.g. 10 minutes of arc) by each revolution of the endless screw with which it gears. The screw is worked by a treadle, and the machine can be so adjusted that a movement of the treadle shall secure either the whole or any desired part of a revolution of the screw.
A dividing engine was invented by Troughton, but it was exceedingly complicated. That of Simms, which was self-acting and threw itself out of gear when its work was done, takes a high place among mechanical inventions. The most accurate of the early graduation machineswas that produced in 1831 by Andrew Ross. For fine graduation Proment invented a machine in which the object to be graduated was slowly and intermittingly pushed forward by a screw, while a fine steel or diamond point, working automatically, made a cut at each cessation of the feeding motion. He thus drew 25,000 lines marking equal intervals in the space of one inch, but the number was since increased to 225,000 by Nobert. These nachines now appear very crude since the advent of modern electronics and the laser. Research Graduation
Halo is the name given to coloured circles of light sometimes seen round the sun or moon, and to other connected luminous appearances. These phenomena are classified as: (1) Halos proper, consisting of complicated arrangements of arcs and circles of light surrounding the sun or moon, accompanied by others tangent to or intersecting them; (2) coronas, simple rings, generally somewhat coloured; (3) aureolas, the name given to the kind of halo surrounding a shadow projected upon a cloud or fog-bank, or to the coloured rings observed by aeronauts on the upper surface of clouds. All these appearances are the result of certain modifications which light undergoes by reflection, refraction, dispersion, diffraction, and interference when it falls upon the crystals of ice, the raindrops, or the minute particles that constitute clouds. Research Halo
In geometry, a triangle is any figure formed by three intersecting lines. When the lines are straight the triangle is a plane triangle. In spherical triangles, the sides are arcs of great circles of a sphere. Triangles are called equilateral, isoceles and scalene, according as all three sides are equal, two sides are equal, or all sides are unequal. The first book of Euclid is concerned chiefly with the properties of plane triangles, and from the study of such properties arose the science of trigonometry. The area of a plane triangle is half the length of the base multiplied by the altitude of the apex or the square root of s(s-a)(s-b)(s-c) where a,b and c are the lengths of the sides, and s is half their sum.
The Probert Encyclopaedia was designed, edited and programed by
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Abbreviations
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