Twierdzenie Weyer’a i jego zastosowanie w rozwiązywaniu wybranych zadań

• Autorzy: Wojtowicz B.

Warianty tytułu

EN

Weyer's theorem and its application to solve certain problems

• Języki publikacji: PL

Abstrakty

EN

One of the important theorems concerning a bundle of conics is the one recognized as Weyer's theorem, or a generalized second Desargues' theorem [ 1 ]. The theorem may be expressed as follows. Weyer's Theorem. If a bundle of conics p2~,~, N (a2 , b2 , c 2 , .....) with four base points I, II, III and IV will be intersected with a conic k2 which does not belong to the given bundle, but which passes through the two out of four of the given base points, then the conics of a bundle p 2 (a2 , b2 , c 2 , .....) intersect with the conic k2 at points of an involutory chain of points of the second order k2 (A1 A2, B1B2, C1C2, ...). Let us notice that if a conic k2 passes through the two out of four of the given base points of a bundle of conics then the center of involution O (point of intersection of lines a = A1A2, b= B1B2, .....) lies in the opposite side of the quadrangle I, II, III, IV. The last property can be utilized to solve certain tasks on circles or bundles of circles. Let, for example, be assumed that such a circle is to be constructed that passes through a given real point and two imaginary points belonging to an optional line. Certain problems related to Weyer's theorem are discussed in the paper.

Słowa kluczowe

PL

twierdzenie Weyer'a; geometria wykreślna; grafika inżynierska

EN

Weyer’s theorem; descriptive geometry; engineering graphics

• Wydawca: Polskie Towarzystwo Geometrii i Grafiki Inżynierskiej
• Czasopismo: Materiały Seminarium Geometrii i Grafiki Inżynierskiej
• Rocznik: 1999
• Tom: z. 8
• Strony: 58--62

Twórcy

autor

Wojtowicz B.

• Samodzielna Pracownia Geometrii Wykreślnej i Grafiki Inżynierskiej Politechnika Krakowska