DE914439C - Auxiliary device for the graphical determination of the circumference and content - Google Patents

Auxiliary device for the graphical determination of the circumference and content

Info

Publication number
DE914439C
DE914439C DESCH865D DESC000865D DE914439C DE 914439 C DE914439 C DE 914439C DE SCH865 D DESCH865 D DE SCH865D DE SC000865 D DESC000865 D DE SC000865D DE 914439 C DE914439 C DE 914439C
Authority
DE
Germany
Prior art keywords
circumference
auxiliary device
content
angle
graphical determination
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired
Application number
DESCH865D
Other languages
German (de)
Inventor
Ernst Schoepfer
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
ERNST SCHOEPFER
Original Assignee
ERNST SCHOEPFER
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by ERNST SCHOEPFER filed Critical ERNST SCHOEPFER
Priority to DESCH865D priority Critical patent/DE914439C/en
Application granted granted Critical
Publication of DE914439C publication Critical patent/DE914439C/en
Expired legal-status Critical Current

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Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B43—WRITING OR DRAWING IMPLEMENTS; BUREAU ACCESSORIES
    • B43L—ARTICLES FOR WRITING OR DRAWING UPON; WRITING OR DRAWING AIDS; ACCESSORIES FOR WRITING OR DRAWING
    • B43L7/00—Straightedges
    • B43L7/027—Plural non-adjustable straightedges fixed at right angles
    • B43L7/0275—Triangles

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  • Image Analysis (AREA)

Description

Aufgabe der Erfindung ist ein Hilfsgerät zur graphischen Ermittlung des Kreisumfanges und Kreisinhaltes.The object of the invention is an auxiliary device for graphical determination the circumference and content of the circle.

Die Lösung besteht aus einer Dreieckschablone, die einen Winkel aufweist, dessen Cosinus gleich ist. Eine weitere Lösung ist eine Winkelschablone, deren einer Winkel so gewählt ist, daß sein Tangens gleich - i ist.The solution consists of a triangle template that has an angle whose cosine is equal is. Another solution is an angle template, one angle of which is chosen so that its tangent is equal - i is.

Das erstgenannte Gerät wird in der Weise verwendet, daß man die eine an dem genannten Winkel angrenzende Seite der Dreieckschablone an eine beliebige Durchmesserlinie des gegebenen Kreises so anlegt, daß die Spitze des Winkels auf seinen Umfang fällt (vgl. Fig. i). Der andere Schenkel des Winkels schneidet dann den Umfang des Kreises im Punkt D. Die Strecke A -D stellt dann die Seite des dem Kreis inhaltsgleichen Quadrates dar. Es ist nämlich A-D = A-B - cos a. A-B ist aber gleich 2 r, cos a erfindungsgemäß gleich Es ist also A-D = und A-D`-' = r2 ic. Fällt man vom Punkt D auf den Durchmesser A-B die Senkrechte, so hat der Fußpunkt C dieser Senkrechten auf dem Durchmesser von A einen Abstand, der gleich einem Viertel des Kreisumfanges ist. Es ist nämlich Das zweite Gerät wird in derselben Weise an den zu vermessenden Kreis angelegt (vgl. Fig. 2). Es wird jedoch in diesem Falle der Schnittpunkt P des zweiten Schenkels mit dem auf dem ersten Schenkel senkrechten Durchmesser (A-B) festgelegt. Die Strecke A-P ist dann gleich einem Viertel des Kreisumfanges. Beweis: M-P = E-M - tgß , E-M=y, The first-mentioned device is used in such a way that the one side of the triangular template adjoining the mentioned angle is applied to any diameter line of the given circle in such a way that the tip of the angle falls on its circumference (see FIG. I). The other leg of the angle then intersects the circumference of the circle at point D. The line A -D then represents the side of the square with the same content as the circle. This is because AD = AB - cos a. However, AB is equal to 2 r, cos a is equal according to the invention So it is AD = and AD`- ' = r2 ic. If the perpendicular falls from point D to the diameter AB, the base point C of this perpendicular on the diameter of A is at a distance equal to a quarter of the circumference. Because it is The second device is applied to the circle to be measured in the same way (see FIG. 2). In this case, however, the point of intersection P of the second leg with the diameter (AB) perpendicular to the first leg is determined. The distance AP is then equal to a quarter of the circumference. Proof: MP = EM - tgß , EM = y,

Claims (3)

PATENTANSPRÜCHE: i. Hilfsgerät zur graphischen Bestimmung des Kreisumfanges und Kreisinhaltes, dadurch gekennzeichnet, daß es aus einer Dreieckschablone besteht, die einen Winkel aufweist, dessen Cosinus gleich ist. PATENT CLAIMS: i. Auxiliary device for the graphic determination of the circumference and the contents of a circle, characterized in that it consists of a triangular template which has an angle whose cosine is the same is. 2. Gerät nach Anspruch i, dadurch gekennzeichnet, daß ein weiterer Winkel der Dreieck-Schablone 9o° beträgt. 2. Apparatus according to claim i, characterized in that a further angle of the Triangle template is 9o °. 3. Hilfsgerät zur graphischen Bestimmung des Kreisumfanges, dadurch gekennzeichnet, daß es aus einer Winkelschablone besteht, deren einer Winkel so gewählt ist, daß sein Tangens gleich - i ist.3. Auxiliary device for the graphical determination of the circumference, characterized in that it consists of an angle template, one angle of which is chosen so that its tangent is equal - i is.
DESCH865D 1943-09-17 1943-09-17 Auxiliary device for the graphical determination of the circumference and content Expired DE914439C (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
DESCH865D DE914439C (en) 1943-09-17 1943-09-17 Auxiliary device for the graphical determination of the circumference and content

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
DESCH865D DE914439C (en) 1943-09-17 1943-09-17 Auxiliary device for the graphical determination of the circumference and content

Publications (1)

Publication Number Publication Date
DE914439C true DE914439C (en) 1954-07-01

Family

ID=7422593

Family Applications (1)

Application Number Title Priority Date Filing Date
DESCH865D Expired DE914439C (en) 1943-09-17 1943-09-17 Auxiliary device for the graphical determination of the circumference and content

Country Status (1)

Country Link
DE (1) DE914439C (en)

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