## Elements of Geometry and Trigonometry |

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Page 13

From one point to another only one straight line can be

From one point to another only one straight line can be

**drawn**. 12. Through the same point , only one straight line can be**drawn**which shall be parallel to a given line . 13. Magnitudes , which being applied to each other , coincide ... Page 18

If from any point within a triangle , two straight lines be

If from any point within a triangle , two straight lines be

**drawn**to the extremities of either side , their sum will be less than the sum of the two other sides of the triangle . Let any point , as O , be taken within the trian- gle BAC ... Page 20

The equality of the triangles BAD , DAC , proves also that the angle BAD , is equal to DAC , and BDA to ADC , hence the latter two are right angles ; therefore , the line

The equality of the triangles BAD , DAC , proves also that the angle BAD , is equal to DAC , and BDA to ADC , hence the latter two are right angles ; therefore , the line

**drawn**from the vertex of an isosceles triangle to the middle ... Page 22

From a given point , without a straight line , only one perpendicu lar can be

From a given point , without a straight line , only one perpendicu lar can be

**drawn**to that line . Let A be the point , and DE the given line .. B E Let us suppose that we can**draw**two perpendiculars , AB , AC . Page 23

Produce the perpendicular AB till BF is equal to AB , and

Produce the perpendicular AB till BF is equal to AB , and

**draw**FC , FD . First . The triangle BCF , is equal to the triangle BCA , for they have the right angle CBF CBA , the side CB common , and the - D side BF = BA ; hence the third ...### What people are saying - Write a review

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### Other editions - View all

Elements of Geometry and Trigonometry from the Works of A. M. Legendre A. M. Legendre No preview available - 2017 |

### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole