Uzmig

Deg Tanzeggit tuglimt , Uzmig d uzlig i d-ikkan seg uzdiger n ukaswar K {\displaystyle K} usbiṭ ur d-izerri ara seg yixef n K {\displaystyle K} yerna ur t-ittnali ara (azdiger deg snat n tegnatin-a d agaz neɣ d amaɣad).

Uzmigen ttwazrawen seg wakud amzikan (200 st ) ass mi i d-igra Apolonio n Perga tazrawt i d-immalen aylanen-is

Tanzeggit taklidant

Asenmel aseldan

Uzmig di tesledt tasnakant d adeg anzeggan i wagaz yettewliwlen, anda assaɣ gar n yiseggiwen-is ɣef wagaz usbiṭ d useggiw-is ɣef umaɣad usbiṭ d assaɣ usbiṭ. assaɣ-a yettusemma s wallunmas (Eccentricity), ma d agaz usbiṭ isem-is adik , ma d amaɣud ittusemma turwin (directrix).

P S = e . P M {\displaystyle PS=e.PM}

Anda:

- P d agaz (x,y) tezga-d deg uglay.

- S d adik

- e d amuskir n wallunmas

- ma d m d timbeddit taratakt n P ɣef turwin.

Ma yella wallunmas yegda tigget, ad yettwasemmi s tkenzirart , ma yella ddaw n tigget ad yettwasemmi aglay , ma yella yugar tigget ad yettwasemmi tafeljumma . Dɣa takenzirart d uglay d tfeljumma isem-it-sent uzmigen acku zemren ad nnulfan s usrag n uzdiger n wegni ɣef kra n waddad.

Tilmas n wuzmigen

Llant 3 n telmas ( Aglay , Takenzirart d tfeljumma ). Ma d tawinest tezmert ad tettwimeggez d talmest tis 4 (akken iy ɣil Apolonio ), neɣ yezmer ad yili fell-as umeggez d akken-itt d talmest seg uglay. Dɣa aglay d twinest ttwasilɣen-d mi ara ad yili uzdiger n ugniw yakk d ukawsar d amezlagu umdil. Ma d tawinest tettwasileɣ-d mi ara ad yili ugniw azdigran yemsideɣ i twinest n uzadur i d-isnulfan akaswar.

Iẓalayen

Deg Tanzeggit tuglimt , Uzmig d uzlig i d-ikkan seg uzdiger n ukaswar K {\displaystyle K} usbiṭ ur d-izerri ara seg yixef n K {\displaystyle K} yerna ur t-ittnali ara (azdiger deg snat n tegnatin-a d agaz neɣ d amaɣad).

Uzmigen ttwazrawen seg wakud amzikan (200 st ) ass mi i d-igra Apolonio n Perga tazrawt i d-immalen aylanen-is

Tanzeggit taklidant

Asenmel aseldan

Uzmig di tesledt tasnakant d adeg anzeggan i wagaz yettewliwlen, anda assaɣ gar n yiseggiwen-is ɣef wagaz usbiṭ d useggiw-is ɣef umaɣad usbiṭ d assaɣ usbiṭ. assaɣ-a yettusemma s wallunmas (Eccentricity), ma d agaz usbiṭ isem-is adik , ma d amaɣud ittusemma turwin (directrix).

P S = e . P M {\displaystyle PS=e.PM}

Anda:

- P d agaz (x,y) tezga-d deg uglay.

- S d adik

- e d amuskir n wallunmas

- ma d m d timbeddit taratakt n P ɣef turwin.

Ma yella wallunmas yegda tigget, ad yettwasemmi s tkenzirart , ma yella ddaw n tigget ad yettwasemmi aglay , ma yella yugar tigget ad yettwasemmi tafeljumma . Dɣa takenzirart d uglay d tfeljumma isem-it-sent uzmigen acku zemren ad nnulfan s usrag n uzdiger n wegni ɣef kra n waddad.

Tilmas n wuzmigen

Llant 3 n telmas ( Aglay , Takenzirart d tfeljumma ). Ma d tawinest tezmert ad tettwimeggez d talmest tis 4 (akken iy ɣil Apolonio ), neɣ yezmer ad yili fell-as umeggez d akken-itt d talmest seg uglay. Dɣa aglay d twinest ttwasilɣen-d mi ara ad yili uzdiger n ugniw yakk d ukawsar d amezlagu umdil. Ma d tawinest tettwasileɣ-d mi ara ad yili ugniw azdigran yemsideɣ i twinest n uzadur i d-isnulfan akaswar.

Iẓalayen

Allunmas (awlilles)

Llant snat n turwin d sin n wadiken i tekenzirart d uglay. Ameccaq gar n wammas d turwin a / e {\displaystyle a/e} , ma a {\displaystyle a\ } iga d azengellus ameqran d umeẓyan n uglay, neɣ ameccaq gar n wammas ɣer yixef n tfeljumma. Ameccaq seg wammas ɣer wadik a e {\displaystyle ae\ } .

Deg tegnit n twinest yettili umuskir n wallunmas e = 0.

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