## Chauvenet's Treatise on Elementary Geometry |

### From inside the book

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**Corollary**I. If one of the two adjacent angles which one line makes with another is a right angle , the other is also a right angle . 13.**Corollary**II . If a line CD is perpen- dicular to another line AB , then , reciprocally , the line ... Page 15

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**Corollary**I. If one of the two adjacent angles which one line makes with another is a right angle , the other is also a right angle . 13.**Corollary**II . If a line CD is perpen- dicular to another line AB , then , reciprocally , the line ... Page 25

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**Corollary**L. The alternate - exterior angles , AGE and DHF , being equal to their vertical angles , HGB and GHC , are also equal to each other . 51.**Corollary**II . Any one of the eight angles is equal to its cor- responding angle . Thus ... Page 26

William Chauvenet. 56

William Chauvenet. 56

**Corollary**II . If the sum of the two interior angles on the same side of the secant line is equal to two right angles , the two lines are parallel . 57.**Corollary**III . From ( 52 ) and ( 56 ) it follows that , when ... Page 27

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**Corollary**I. Two angles , as ABC and D'EF ' , having their sides parallel and lying in opposite directions ( that is ED ' opposite to BA and EF ' opposite to BC ) , are equal . For we have D'EF ' DEF АВС . = 62.**Corollary**II . Two ...### Other editions - View all

### Common terms and phrases

ABCD adjacent angles allel angle AOB angle BAC angles are equal apothem arc AC BC² bisector bisects called centre chord circum circumference coincide Corollary Definition diagonals diameter dicular distance divided draw equal angles equally distant exterior angle ference figure four right angles geometry given angle given point given straight line greater hence homologous sides hypotenuse inscribed inscribed angle intercepted arcs less Let ABC measured by one-half middle point number of sides oblique lines one-half the arc opposite sides parallel to BC parallelogram pendicular perimeter perpen perpendicular points of intersection produced proportion PROPOSITION quadrilateral quantities radii radius ratio rectangle regular polygon rhombus right angles right triangles Scholium secant line segment semi-circumference side AC sides are equal square straight line drawn symmetrical with respect tangent theorem triangle ABC triangles are equal vertex

### Popular passages

Page 201 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 31 - The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP

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Page 120 - Any side of a spherical triangle is less than the sum of the other two.

Page 81 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.

Page 92 - Every point in the bisector of an angle is equally distant from the sides of the angle...

Page 58 - An angle formed by a tangent and a chord is measured by one-half the intercepted arc.