Bion, Nicolas
,
Traité de la construction et principaux usages des instruments de mathématique
,
1723
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USAGE DES PREMIERS
"/>
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<
head
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xml:space
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">USAGE III.</
head
>
<
head
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style
="
it
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xml:space
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preserve
">Abaiſſer une perpendiculaire ſur une ligne donnée d'un point
<
lb
/>
hors de ladite ligne.</
head
>
<
p
>
<
s
xml:id
="
echoid-s730
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xml:space
="
preserve
">SOit le point donné C, duquel il faut abaiſſer une perpendicu-
<
lb
/>
<
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position
="
left
"
xlink:label
="
note-026-01
"
xlink:href
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note-026-01a
"
xml:space
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preserve
">Fig. 6.</
note
>
laire ſur la ligne A B.</
s
>
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s
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xml:space
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</
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<
p
>
<
s
xml:id
="
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xml:space
="
preserve
">Du point C, comme centre, décrivez un arc de cercle qui coupe
<
lb
/>
la ligne A B en deux points D E; </
s
>
<
s
xml:id
="
echoid-s733
"
xml:space
="
preserve
">de ces points D & </
s
>
<
s
xml:id
="
echoid-s734
"
xml:space
="
preserve
">E, faites la
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Section F, & </
s
>
<
s
xml:id
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xml:space
="
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">mettant la Regle ſur les points C & </
s
>
<
s
xml:id
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echoid-s736
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xml:space
="
preserve
">F, tirez la per-
<
lb
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pendiculaire C G.</
s
>
<
s
xml:id
="
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xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
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preserve
">On peut faire la Section F au-deſſus ou au deſſous de la ligne
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donnée; </
s
>
<
s
xml:id
="
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xml:space
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">mais il eſt bon qu'elle ſoit au-deſſous, parce que les points
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C & </
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>
<
s
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xml:space
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">F étant éloignez, on tire plus juſtement la perpendiculaire
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lb
/>
que s'ils étoient proches.</
s
>
<
s
xml:id
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xml:space
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"/>
</
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>
<
p
>
<
s
xml:id
="
echoid-s742
"
xml:space
="
preserve
">Que ſi la portion de cercle décrite du point C ne coupe pas la
<
lb
/>
ligne A B en deux points, il faudra continuer la ligne, s'il ſe peut;
<
lb
/>
</
s
>
<
s
xml:id
="
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xml:space
="
preserve
">ſinon il faudra ſe ſervir de la derniere methode ci-devant rapportée
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pour élever une perpendiculaire à l'extremité d'une ligne; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">car dans
<
lb
/>
la même figure 5, ſuppoſé qu'on veuille abaiſſer une perpendicu-
<
lb
/>
laire du point D ſur la ligne C B, tirez à volonté la ligne D B, divi-
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ſez-la en deux également au point P; </
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>
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">de ce point comme centre, & </
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de l'intervalle P D, décrivez l'arc D C B, coupant la ligne A B au
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/>
point C; </
s
>
<
s
xml:id
="
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xml:space
="
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">poſez la Regle ſur les points C & </
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">D, & </
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xml:space
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">tirez la ligne
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/>
C D, elle ſera la perpendiculaire requiſe.</
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>
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xml:id
="
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xml:space
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"/>
</
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<
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<
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">Autrement. </
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>
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">Soit la ligne A B & </
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>
<
s
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xml:space
="
preserve
">le point donné C hors icelle,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-026-02
"
xlink:href
="
note-026-02a
"
xml:space
="
preserve
">Fig. 7.</
note
>
duquel il faut abaiſſer une perpendiculaire. </
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>
<
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xml:space
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">Prenez les deux points
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1 & </
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xml:space
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">2 à volonté ſur ladite ligne A B; </
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">puis des points 1 & </
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">2 & </
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>
<
s
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xml:space
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">des
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intervalles 1 C & </
s
>
<
s
xml:id
="
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xml:space
="
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">2 C, décrivez des arcs de cercles qui s'entrecou-
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peront en deux points; </
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>
<
s
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xml:space
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">ſçavoir, une fois au point C, & </
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>
<
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">l'autre
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fois au point D, au-deſſous de la ligne; </
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>
<
s
xml:id
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xml:space
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">poſez la Regleſur les deux
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interſections, & </
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>
<
s
xml:id
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xml:space
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">tirez une ligne qui ſera perpendiculaire ſur la li-
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gne A B.</
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xml:space
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</
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<
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xml:space
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">USAGE IV.</
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>
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style
="
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xml:space
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">Couper un angle rectiligne en deux également.</
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<
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>
<
s
xml:id
="
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xml:space
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preserve
">SOit A C B l'angle qu'il faut couper en deux angles égaux.
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</
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<
note
position
="
left
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xlink:label
="
note-026-03
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xlink:href
="
note-026-03a
"
xml:space
="
preserve
">Fig. 8.</
note
>
</
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<
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<
s
xml:id
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xml:space
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">Du point C, comme centre, décrivez l'arc D E à volonté:</
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>
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<
unsure
/>
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des points D & </
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<
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xml:space
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</
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