US381049A - Adolfo saenz yanez - Google Patents

Description

(No Model.)

7 8 H s., AfiEz. INSTRUMENT FOR DIVIDING ANGLES}. No. 381,04 9.

gavte ntgd Apr. 10, 1888,

INVENTOR:

$5 M) I v v ATTORNEYS N. PETERS, Pinto-mum Wallinghm D. C.

. and details and combinations of the same, as

ADOLFO sAnNz 'YANEZ, on NEW YORK, N. Yl f INSTRUMENT FOR olvlome'AueLes'.

sPBcI PIcATIoN forming part of Letters Patent No. 381,049, dated April'lO, 188a. Application filed October 16,1886. Serial Ne. 216,419. No model.)

To aZZ whom it may concern.- Be it known that I, ADOLFO SAENZ YAIQEZ, (a subject of the King of Spain,) of Havana, Cuba, at present residing inthe city, county, and State of New York, have invented a new and Improved Instrument for Dividing Sectors, of which the following is a full, clear, and

exact description.

The object of my invention is to. provide a new and, improved instrument for dividing sectors and angles into equal parts, and I prefer to call the instrument a polysector.

The invention consists of a plate provided with polysecting curves.

The invention also consists in various parts will be fully described hereinafter, and then pointed out in the claims; 1 7

Reference is to be had to the accompanying drawings, forming .a part of'this specification,

'in which similar letters of reference indicate corresponding parts in all the figures.

Figure 1 is a face view of my improvement for dividing angles or sectors into equal parts. Figs. 2'and 3 are'similar views showing polysecting curves of different forms.

The instrumen'tismade of a thin plate, A, and is "preferably provided with the semi-Cir: cle B, and having its "center at 0, through which passes a diameter, D, whichforms the base of the instrument. A second concentric semi-circle,a,is inside of the semi-circle B and unites at F and G with the baseline D. A number of polysecting curves, 11,0, d, and e,are arranged within the polyseeting circle a and the base D, and the part between the semi-cir cle a and the first polysecting curve, I), is cut out of the plate A, and the space of the plate A between the polysecting curve 0 and the next polysecting curve, d, is removed, and the space between the next curve, e, and the baseline D havea proportionate relation with each other secting curves.

is similarly cut out, so that bands are formed the edges of which represent the saidpoly- All the bands thus formedeonnect with a base-band, E, which extends be low the base D. The polysecting curves ter minate either with one endat a common point The curve 6 is determined under the condition that the that the for' eachinstrum'entybut the instrument can be provided with different forms of curves,- as shown in the figures, in which Figs. 1 and 3 TED STATESv show almond and apple shaped curves, while in Fig. 2 I make use of hyperbolas to attain the same purpose. I

The curve I) in Fig. 1 is defined geometrically under the condition that any one of its points--for instance, Oproduces-the equ'aangle F00 6 1 tion =1 The curve 0 1s simllarly defined under the condition that the M2941 angle P G '3F 3- 8 under the condition that the ang 4 angle FTC 9 angle 00F angleoFO I mined under theconditionthat g-::%% I, the curve at under the condition that angle 'qOF W determined under tthe conditionrthat ,the

angle rCE 5 angle TF0 rhef'eurve a is defined =4. The curvee is geometrically InFig. 3 theeu-rves (1, 1), 0, d, and fe are I angle CFn 5" the curve a, that the angle CEO 4.

is part of acirclewhich has its "central point at ,o, the radius being no. The curve d J --similarly determined under the condition, for

. 9 curve 12 .under the condition that the 2; thefjcurve a under the conis defined under .the condition that the angle GFq 2 1 angle FgO Z termined under angle CFr 1 angle FrO o".

a-ndthe curve e'gis" do: the condition ithatihe;

The curve a is deter- A straight-edge, N, is preferably used in connection with the instrument, and is provided with a point in line with one of its edges and fitted into an aperture into the plate A at the point F. A knob or button, N, is fastened near the other end of the straightedge and serves to swing the said straightedgeN over the front of the plate A, the point F being the axis.

The instrument is used as follows: When the angle 0G]? is to be divided into equal parts, then the instrument is placed over the angle with the point 0 on the intersection of the lines 00 and PO, and the base D of the instrument is on the line PC. It will be seen that the line 00 intersects with all the polysectin g curves a, b, 0', d, and e at the points a, o, p, q, and r, and the operator now places the straight-edge N on the point 0 and marks with a pencil or other means the intersection of the straight-edge with the semi-circle a at the point 1. The operator then swings the straight-edge N to the point p and marks the intersection of the straight-edge N on the semicircle a at 2. Then the straight-edge N is moved to the point q, and the point Sis marked on the semi-circle a, after which the operator marks in a similar manner the point 4 by swinging the straight-edge to the point r. The points 1, 2, 3, and 4 are equidistant from each other on the part nG of the semi-circle a, and

. if the operator now removes the instrument and draws the lines RC, R0, R 0, R 0, then a division of the angle 0GP into five equal angles is made, and a sector constructed on the said angle by drawing the respective arc is divided into five equal parts. The same angle, 0GP, can also be dividedinto four equal SO, 8'0, and S 0 are drawn and the requireddivision into four equal parts is obtained. The angle is in a similar manner divided into three or two equal parts by indicating the respective points of the polysecting curves 0 and din a manner similar to that described above.

To prove that the points 1, 2, 3, and 4 divide the arc of the circle nG into five equal parts, Fig. 1, the following considerations will be sufiicient: In the triangle F00, formed in l the curve I), we have angle oFC-tangle FOG:

angle 0GP, for the reason that this last angle is the external angle, that in said triangle is opposite to the two first angles. Also, we have angle F00 =2 angle oFG in consequence of the geometrical definition of the curve I). From the union of these two equations we deduce with respect to the triangle pFO, formed in angle F190 7 the curve 0, in which we reach 3 the following equation: angle 2CG= angle oCP'" "1(2). Inthe curved, astudy ofthesame an leF C 8 kind,consideringtl1at g howsthat angles 3OG= angle 0CP-:"'"(3). Finally, in

angle F'rC the curve 6, where we know thatthe W:

' 1 g the same reasoning gives angle 40G angle An examination of the above equations- 1, 2, 3, and 4-enables us to see that we have angle nCl==angle 1G2=angle 203=angle 3C4 angle 40G angle 0GP, with which it is evident that the arcs n1,1 2, 2 3, 34, 4G are equal to each other, and that each one is the fifth part of the arc nG.

It is to be observed that the first polysecting curves give the division into five parts, the second curve the division into four parts, the third division into three parts, and the fourth the division into two parts. All the divisions maybe obtained simultaneously before removing the instrument.

The characteristic property of the polysecting curves at, b, c, d, and e consists in the constant or invariable relation of two of the angles of the triangle formed by thelines which unite the two points F and O to any one point of the curves. In Figs. 1 and 3 this constant relation is established for all the curves between the angle 0pposite the common base FC and the angle which has its vertex in the point F. In Fig. 2 a constant relation is between the angles adjacent to the base F0. Hence it is seen that a constant relation exists between the two angles drawn from F and from O to any two points located on any of the curves. For exaniple: In the curve b, Fig. 1, the angle 0FC= angle 00G, and when the line 80 is drawn it is found that the angle WC- 5% angle 80G. Now a deduction of the result of the two equations gives angle 0FCangle sFG= (angle 0OG-angle 'sCG) or angle oFsz angle 00s, thus demonstrating the relation between the two angles. As the angles 1F2, 2F3, 3E4, and 4FG are 381,049 j i a v The instruments represented in Figs; 2 and i equal,-as before stated, it follows that the four I used in the same rnanner' described in 5'.

angles 00s, sGs, sOs and 820G havea'like re-' 3 are curve 0 each have a value of lation to each other, all angles beingthe result of the property of the curve bin consequence of the value of each angle being of the angle 1F2.' The three angles produced by the angle 1E2,- and the two angles produced on curve 1 each have a valueof angle 1E2 As the angle 1s equa to 10 7 each one of the angles obtained by means of the curve 12 has a value of x angle 00]? or 2 angle 0GP, and each angle of 1 those pertaining to curve 0 has a value of angle 0UP, and

each angle of those belonging to the curve d has a value of angle 0GP. 7

It will thus beseen that when an instrumentreference to'Fig. 1.

Instead of using the straight-edge, a? com mon ruler may be employedfor the same purposeand in the same manner.

Having thus described my invention, what I claim as new, and desire to secureby Letters 3 secting curves, substantially as shown and described.

2. An instrument for dividing angles and sectors,.consisting of a frame having theedge D forming a base and provided with a number of bands; the edges of which are polysecting curves, substantially as shown and described, v

3. In an instrument for dividing anglesand sectors, a frame having the edge D forming a base and provided with a number of bands,

the edges of which are polysecting curves, in

combination with a straight-edge pivoted on the-said frame,- substantially as shown an'dde scribed.

I ADOLFQ' sAENZ YA N Ez.

Witnesses:

A. E. BEACH,

EDGAR (TATE; q

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