## Elements of geometry: consisting of the first four,and the sixth, books of Euclid, with the principal theorems in proportion [&c.] by J. Narrien1842 |

### From inside the book

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**cylinders**and cones : they contain also demonstrations of the ratios that circles and spheres , respectively , bear to one another . Lastly , the thirteenth book relates to equilateral and equiangular figures inscribed in circles , and ... Page

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**cylinders**, cones , and spheres ) , differ from those which , in the editions just men- tioned , and in that of Dr. Simson , are employed in propo- sitions relating to such figures : and , without departing from the spirit of the ... Page

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**cylinder**is equal in volume to three times the volume of a cone having an equal base and an equal altitude ; and the process may be generalised in the following manner . Let the**cylinder**be represented by A , and the cone by B ; and let ... Page

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**cylinder**or the cone raised upon the circle as a base , by volumes and surfaces less than the least that can be ...**cylinders**formed by the revolution of rect- angles inscribed within , and described about the circle by whose revolution ... Page 239

... are to one another in the duplicate ratio , or as the squares , of their homologous sides , and consequently of the perpendiculars PQ , pq . ELEMENTS OF GEOMETRY . ON THE

... are to one another in the duplicate ratio , or as the squares , of their homologous sides , and consequently of the perpendiculars PQ , pq . ELEMENTS OF GEOMETRY . ON THE

**CYLINDER**, THE CONE PRISMS , ETC. 239 OF GEOMETRY .### Other editions - View all

Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides No preview available - 2015 |

Elements of Geometry: Consisting of the First Four, and the Sixth, Books of ... Euclides No preview available - 2018 |

Elements of Geometry: Consisting of the First Four,and the Sixth, Books of ... Euclides No preview available - 2013 |

### Common terms and phrases

ABCD AC is equal adjacent angles altitudes angle ABC angle ACB angle BAC assigned base BC bisected centre circle ABC circumference cone convex surface cylinder described diameter draw drawn duplicate ratio Edition equal angles equal or equivalent equi equilateral and equiangular Euclid exterior angle fore given line given rectilineal given straight line gnomon greater Greek homologous homologous sides inscribed join Latin Let ABC measure number of sides opposite angles parallel parallelepiped parallelogram perpendicular picket plane angles prism PROB proportional proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure regular polygon remaining angle right angles segment similar solid angle sphere spherical angle square of AC straight line AC THEOR touches the circle triangle ABC triangle DEF wherefore

### Popular passages

Page 55 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.

Page 47 - CB ; wherefore the four figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB: therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line, &c.

Page 12 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity...

Page 73 - CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED.

Page 8 - A New Treatise on the Use of the Globes ; or, a Philosophical View of the Earth and Heavens : comprehending an Account of the Figure, Magnitude, and Motion of the Earth: with the Natural Changes of its Surface, caused by Floods, Earthquakes, &c.

Page 142 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 11 - ABC is therefore equal to the remaining angle ACB, which are the angles at the base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB, which are the angles upon the other side of the base. Therefore, " the angles at the base

Page 53 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Page 30 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.

Page 9 - If two triangles have two sides of the one equal to two sides of the...