Proposition IV.1 — Into a given circle to fit a straight line equal to a given …

Proof

Let

A B C

be the given circle and

D

the given segment, not greater than the diameter

B C

of the circle. Apply I.3 to cut off from

B C

a segment

B E

equal to

D

. With centre

B

and radius

B E

describe a circle

E A F

(Postulate 3); join

B A

where

E A F

meets the given circle. Then

B A = B E = D

by Definition I.15, so

B A

is the required chord.

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Full neighborhood

Depends on (3)

I.3Proposition I.3Given two unequal straight lines, to cut off from the greater a straight line equal to the less.
3Postulate 3To describe a circle with any centre and distance.
I.15Definition I.15A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among…

Required by (dependents) (1)

IV.10Proposition IV.10To construct an isosceles triangle having each of the angles at the base double of the remaining one.

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