## Elementary geometry |

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Resultat 6-10 av 57

Side 44

En . Let EF and GH be parallel straight lines , and let ABCD

required to prove that the alternate angles EBC , BCH are equal . E Proof . For if

EBC were not equal to BCH , let some other line LBM be drawn through B

making ...

En . Let EF and GH be parallel straight lines , and let ABCD

**intersect**them ; it isrequired to prove that the alternate angles EBC , BCH are equal . E Proof . For if

EBC were not equal to BCH , let some other line LBM be drawn through B

making ...

Side 45

If a straight line

alternate angles equal , or a pair of ... En . Let the straight line ABCD

two straight lines EF , GH , and make the alternate angles EBC , BCH equal ; then

...

If a straight line

**intersects**two other straight lines and makes either a pair ofalternate angles equal , or a pair of ... En . Let the straight line ABCD

**intersect**thetwo straight lines EF , GH , and make the alternate angles EBC , BCH equal ; then

...

Side 46

... to prove that A is parallel to B . Proof . If A intersected B , then two

lines , A , B would each be parallel to a third line X , which is impossible , by

Axiom 5 . Therefore A does not

... to prove that A is parallel to B . Proof . If A intersected B , then two

**intersecting**lines , A , B would each be parallel to a third line X , which is impossible , by

Axiom 5 . Therefore A does not

**intersect**B , that is , A is parallel to B . Q . E . D ... Side 59

Give the derivation of the words parallel , parallelogram , trapezium . 2 . What is

indirectly ascertained in Theorem 21 ? Would it be possible to ascertain it directly

? 3 . Prove Th . 24 by drawing a straight line to

Give the derivation of the words parallel , parallelogram , trapezium . 2 . What is

indirectly ascertained in Theorem 21 ? Would it be possible to ascertain it directly

? 3 . Prove Th . 24 by drawing a straight line to

**intersect**A , B and X , and using ... Side 64

Let these circles

. For RPQ has its three sides respectively equal to A , B and C * . Limitation . — It

is necessary that any two of. * Euclid , 1 . 22 . 64 ELEMENTARY GEOMETRY .

Let these circles

**intersect**in R . Join RP , RQ . RPQ is the triangle required , Proof. For RPQ has its three sides respectively equal to A , B and C * . Limitation . — It

is necessary that any two of. * Euclid , 1 . 22 . 64 ELEMENTARY GEOMETRY .

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ABCD adjacent angle ABC angle APB angle BAC base bisect bisector Book called centre chord circle circumference coincide College common Constr construct converse Crown 8vo diagonals diameter difference distance divided double draw drawn Edition ELEMENTARY equal angles Euclid Examples exterior angle extremities fall figure Find follows four Geometry given angle given line given point given straight line greater half Hence Illustrations inscribed interior intersect isosceles triangle Join length less Let ABC line drawn locus magnitudes measure meet middle point minor arc opposite sides parallel parallelogram pass perpendicular placed polygon PROBLEM produced Professor Proof proportional quadrilateral radius ratio rectangle contained rectilineal figure regular required to prove respectively right angles School segment Shew sides similar Similarly square supplementary tangent THEOREM third touch triangle ABC unequal

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