Elements of geometry and trigonometry . 132 Co?\ i. Conversely, if thestraight hnes AP, DE, areperpendicular to the sameplane MN, they will be par-allel ; for if they be not so,draw through the point D. aline parallel to AP, this par-allel will be perpendicularto the plane MN ; thereforethrough the same point D more than one perpendicular mightbe erected to the same plane, which is impossible (Prop. 2.). Cor. 2. Two lines A and B, parallel to a third C, are par-allel to each other ; for, conceive a plane perpendicular to theline C ; the lines A and B, being parallel to C, wi
Elements of geometry and trigonometry . 132 Co?\ i. Conversely, if thestraight hnes AP, DE, areperpendicular to the sameplane MN, they will be par-allel ; for if they be not so,draw through the point D. aline parallel to AP, this par-allel will be perpendicularto the plane MN ; thereforethrough the same point D more than one perpendicular mightbe erected to the same plane, which is impossible (Prop. 2.). Cor. 2. Two lines A and B, parallel to a third C, are par-allel to each other ; for, conceive a plane perpendicular to theline C ; the lines A and B, being parallel to C, will be perpen-dicular to the same plane ; therefore, by the preceding Corol-lary, they will be parallel to each other. The three lines are supposed not to be in the same piane ;otherwise the proposition would be already known (Book XXII.). PROPOSITION VIII. THEOREM. If a straight Une is parallel to a straight line drawn in a plane,it will he. parallel to that plane. Let AB be parallel to CDof the plane NM ; then willit be parallel to the plane
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