US2214408A - Proportional divider triangle - Google Patents

Description

SePtflo, 1940- H. A. D v. ARlzPE v 2,214,408

PROPORTIONAT.: DIVIDER TRIANGLE Filed Dec. 19, 1936 Stimmen Patented Sept. 10, 1940 A UNITED STATES 'PATENT orrlcs .3; y PROPORTIONAL DIVIDIER TRIANGLE.

Harmodio A. de Valle Arizpe, Colonia. Portales,

Mexico, D. F., Mexico i v, .y Application December 19, 1936, serialNo. `116,828 i e: i. zolaims. (cia3-104) y t Y This invention relates to improvements'in in- Ahole 'lis made through the triangle at the struments of precision, and its objects are as vertex of the angularly related lines 5, 5. This Ufollow: hole and all similar vholes through the triangle,

.11; First, to. provide an instrument for use by is tapered (Fig. 2) from the inscribed face towardw 5 Y students, draftsmen, and the like, which is so the bottom of the triangle.A This formation read- "5 V constructed and arranged as to enable the Workily admits the sharp point'of Yar pencil and at the ing out and delineation of certain mathematical same time confines the point to a very small area @and geometrical problems involving applied geon the paper underneath. The operator has only .n ometry, and this with speed and accuracy; to insert the point of the pencil When themark,

Second, to provide a simple and accurate deon the paper will appear as little more than adot. "10 vice for the purpose stated above, in which all This dot becomes a reference mark, as presently yof the scales employed are uniform, resulting in appears.

again in accuracy over any such device in which A similar tapered hole 8j is formed in the trithe scales are non-uniform. anglel at the intersection of the base line -5 with 15 I Other objects and advantages will appear from a lineS in continuation of the side2 into the re- "1'5 the following description, reference being made gion of a. horn Ill at the right terminal of the to -the accompanying drawing, in which: triangle. The hypotenuse'line 6 stands at a 45 Figure 1 is a plan view of the improved triinclination toan index jline, II, which is' desangle; 'ignated 90 line.` This line lis perpendicular to Figure 2 is a. detailed cross section taken on the baseline 5, and it is used for the purpose of 2'0 the line 2-2 of Fig. 1; establishing the perpendicularity of any given Figure 3 is a detail cross section taken on the line with respect to the-base line 5. l'line 3-3 of Fig. 1; The face `of the triangle is inscribed with a Figure 4 is a diagrammatic View illustrating number of scales; These occur inrv two general theuse of the triangle in dividing a given line divisions,l one being marked off in a manner sim- 25 i, into a number of equal parts; ilar to .the spacing of a ruler, the other Iconsist- 4 Figure 5 is a diagrammatic view illustrating ing of spaced and numbered holes. It'is confl'the use of the triangle in inscribing a regular templated that in practiceholesother than those polygon in a given circle; t shown will belormed in the'triangle at critically Figure 6 is a diagrammatic view of the triangle and accuratelyllocated places in order to enable 30 illustrating its .use in mapping. the solution of mathematical problems other than This invention lwillbe best understood from a those herein explained. *Thescales -in the first ,consideration of the following detailed descripdivision are designated I2, I3 and I4. The scale y .".tion in view of the accompanying drawing, but I 2 is regularly divided `either inl inches and '"35 it is to be understood that the invention is not fractions thereof-gior, preferably, in centimeters 35 "confined to the disclosure, being susceptible of and millimeters. The scale I2'has l'eft and right such changes and modifications which shall de- .hand origins at the holes 1, 8, as shown'by the fine no material departure from the salient feasets of numbers I5, I6 which occur in increastures of the invention. ing values toward-theindex line II where they The so-called triangle I is intended to be made stop. y t f 40 out of a sheetof Celluloid of a suitable thickness, The scale I2 is ya. scale-of linear ratios or values or any other suitable substitute. In its general and its markings end at one side of a slot I'I n aspect the device is a triangle, but inasmuch which extends in 'parallelism `to the base line 5. as the profile of the side 2 is cut on a curve the This slot has slightly enlarged terminals I8, the ""45winstrument is not a true triangle, but is substanleft hand one of *which occurs directly on a line 45 tially so, and for convenience in reference is t I9 inscribed in the face of the triangle and herein called a triangle. The triangle includes marked 30 line, rinasmuch as this line stands at the base portion 3 and the hypotenusevll. Base a 30. inclination to the base line 5. The line I9 -and hypotenuse lines 5, 6 are inscribed inthe has its origin at the vertex 'I of the angle defined 4-5ojsurface of the triangle at a slight distance in by the lines 5, 6 and II. The purpose of the slot 50 from and parallel to the respective base portion I'I is to enable the insertion offa pencil point so 3, and hypotenuse 4. These lines and all other that armark can be made on the paper opposite inscriptions on the face of the triangle areprefto the desired'ne of the divisions of the scale I2. erably4 lilled with a colored pigment so as to be It is to be observed that the scale I3 is carried easily discernible. out only in part at the opposite extremities of the 55 base of the triangle. The obvious purpose here is to avoid running the scale markings up into the lines 6, I9 at the left and into the markings of the scale I4 at the right. Thus it will be understood that I2 and I3 are one and the same scale, the graduations at the left and right extremities simply branching 01T on opposite sides of the base line 5 to avoid confusion.

The scale I4 in the same division still under discussion is a uniform scale, graduated from to 45 (a little over the 45 being shown). This scale is used in plotting on a map the results of certain surveying operations. Before proceeding with the scales in the Isecond division attention is directed to the structure of the slot II. In order to render the graduations I2 more definitely visible, one edge of the slot is Abeveled at 20 (Fig. 3). This bevel prevents the possibility of a shadow falling on the graduations I2 and thereby insures the visibility of the graduations. As a ymatterrof convenience the graduations I2 and slot Il are supplemented with the designation lines as at 2| so asto enable the user to distinguish from the second division of scales designated circles, as at 22.

T his second division of scales consists of inscribed lines 23, 24, 25,*upon which holes 26, 2'I, 28 are drilled through the triangle and tapered (Fig. 2). The series of holes along the respective lines 23, 24 and 25 are variously spaced and the holes are designated with numbers, as shown. A large hole 29 at a convenient place in the triangle aids the manipulation of the latter.

The use of the various scales is best understood from the description of a rfew examples, it being thought unnecessary to describe more than a few because in actual practice the triangle has many more uses than could be conveniently set out here. Reference is made to Fig. 4 which illustrates the problem of dividing a given line into an equal number of parts, say four equal parts. The given linel 30 is located perpendicularly to the base line 5. This is done by resting the base portion 3 of the triangle I on a T-square and manipulating both until the given line 30 becomes parallel to the index line II, whereupon the triangle I is slid to the right on the edge of the T-square outinto view. Sliding continues until the extremities 3|, 32of the given line 30 coincide with the base and hypotenuse lines 5, 6.

The pencil point isnow used to make a mark 33 on the paper through the hole "I and a second mark 34 on the paper through that hole in the scale line 23 designated bythe numeral 4. By now removing the triangle and using it to guide the pencil point for connecting the marks 33, 34 by a line 35, it will be found that the latter intersects the given line 30 at the point 36 which is one-fourth the length of the given line. The other numerals along the scale line 23 indicate other fractions intov which given lines can be divided.

The next example selected is that of describing a regular polygon within the given circle 37, and reference is made to Fig. for an outline of the operations. The polygon is intended to have nine sides, but the number may be more or less as will be understood from the numeral designations running along the holes in the scale line 24 which is the one now used. The center 38 of the circle is made to coincide with the base line 5, and. the radial line 39 is placed perpendicularly to said base line according to the. method described in connection with Fig. 4.

The triangle I is slid along the edge of the T- square until the circumferential point 40 touches the 30 line I9. A pencil mark 4I is now made on the paper through the hole I and a similar mark 42 is made on the paper through the hole 9, this designating the number of sides of the polygon. A line 43 connecting the marks 4I, 42 if extended far enough beyond the mark 42, Will intersect the circle 3'I at the point 44 which will be found to be one-ninth of the circumference. This measurement can be stepped off, as indicated at 45, and when corresponding measurements are connected by chord lines 46, the resulting gure will be a regular polygon.

A third and last example involves the use of the scale I4 in plotting on a map an observed inclination to the horizon of any given distance remote from a given stadia or observation station of the surveyor. The distance between two stakes or stations, measures `along an inclined distance, is not given on the final map which Will, therefore, show an apparent horizontal distance instead of the true condition of the terrain.

Suppose that the distance between two rods is 750 yards and that the observed vertical angle is 30. According to Fig. 6, the triangle is placed on the map (not shown) in such a manner that the base line 5 coincides with the stadia station, and the course line 5I is perpendicular to said base line. This is accomplished by making the course line 5I coincide with the index line II and by sliding the triangle I along the edge of the T- 'square until the course line is perpendicular to the base line and coincides at the point 41 Where the scale I2 indicates a distance corresponding.

to the intercepted space on the stadi-a rod, in this case '750 yards as indicated at 48.

The horizontal distance is then completed by making a pencil mark 49 on the map through the hole 8, this being the origin of both the right hand side 4of scale I2 and of the scale I4. Another pencil mark 50 is made on the map at the place coinciding with the observed vertical angle, namely 30. By connecting the marks 49, 50 with a line 53 which is extended far enough to intersect the course line 5I, the point 52 Where the intersection occurs denotes the proper reduced distance. Said point 52 will be the next transit station from which to lay off the succeeding course line.

I claim:

l. In an instrument of precision, a triangular body having a base line and a slot parallel to said base line, said body also having van index line perpendicular to the base line, a scale along said mon origin, one line of said pair of lines constituting a base line, a slot in said body parallel to said base line, and a scale between the base line and slot, beginning at said point of origin, said slot beginning at a point Where a perpendicular to said bas line at one of the graduations of said scale intersects the other line of said pair of lines.

HARMODIO A. DE VALLE ARIZPE.

,55 slot, the spacing of the slot from the base line"

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